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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.

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|August 28, 2025
PubMed
Summary
This summary is machine-generated.

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.

Keywords:
Entropic Dynamicsfoundations of Quantum Mechanicsgenerally covariant Quantum Mechanicsproblem of timerelational Quantum Mechanics

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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.