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Entropic Dynamics Approach to Relational Quantum Mechanics.
Ariel Caticha1, Hassaan Saleem1
1Physics Department, University at Albany-SUNY, Albany, NY 12222, USA.
Entropy (Basel, Switzerland)
|August 28, 2025
Summary
Entropic Dynamics (ED) constructs relational quantum mechanics models using inference principles. This framework offers a new measure for state changes and resolves the "problem of time" in quantum gravity.
Area of Science:
- Foundational physics
- Quantum mechanics
- Relationalism
Background:
- Entropic Dynamics (ED) provides a framework for constructing quantum mechanics from inference principles.
- Existing models retain some absolute structures, limiting their applicability to relativistic theories.
- Classical frameworks like Barbour and Bertotti's offer insights but require adaptation for quantum systems.
Purpose of the Study:
- To construct non-relativistic models of relational quantum mechanics using probability, entropy, and information geometry.
- To introduce a novel measure of state mismatch tailored to quantum phase space structures.
- To explore the implications of ED for temporal and spatial relationality and its connection to quantum gravity.
Main Methods:
- Utilizing the Entropic Dynamics framework and principles of inference.
- Developing a new measure of state mismatch based on information metric and symplectic structures.
- Adapting classical intuitions from Barbour and Bertotti's framework to the quantum realm.
- Parametrizing the non-relativistic model into a generally covariant form.
Main Results:
- Construction of non-relativistic quantum mechanics models that are partially relational.
- Explicit demonstration of temporal relationality within ED.
- Development of spatially relational quantum models concerning translations and rotations.
- Identification of quantum constraints on expectation values for relationality.
Conclusions:
- The ED approach offers a viable path to constructing relational quantum mechanics.
- The proposed methods provide a useful testing ground for relativistic theories.
- ED successfully evades the quantum gravity "problem of time" analogue.
- The framework clarifies the quantization of classical constraints for relational theories.
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