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Information-Theoretic Models for Physical Observables.

D Bernal-Casas1, J M Oller1

  • 1Department of Genetics, Microbiology and Statistics, Faculty of Biology, Universitat de Barcelona, 08028 Barcelona, Spain.

Entropy (Basel, Switzerland)
|October 28, 2023
PubMed
Summary

Physical reality is rooted in information theory. This study uses information geometry and quantum harmonic oscillators to show that information is quantized, with the lowest energy state representing reality, supporting the idea that the universe is fundamentally informational.

Keywords:
Bayes’ theoremFisher’s informationRiemannian manifoldsSchrödinger’s equationinformation geometryprinciple of minimum Fisher’s informationquantum harmonic oscillator

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Area of Science:

  • Information theory
  • Quantum mechanics
  • Information geometry

Background:

  • John Archibald Wheeler's concept of the physical as information-theoretic.
  • The need for a mathematical framework to connect information theory and quantum mechanics.

Purpose of the Study:

  • To introduce a novel information-theoretic framework using information geometry.
  • To explore the representation and distribution of information using quantum harmonic oscillators.
  • To investigate the connection between estimator variance, quantum energy levels, and the Cramér-Rao lower bound.

Main Methods:

  • Utilizing information geometry with the Fisher information metric.
  • Applying the time-independent Schrödinger's equation to stationary states.
  • Modeling information sources as quantum harmonic oscillators.
  • Employing Bayes' theorem for posterior probability distribution calculations.

Main Results:

  • Information is represented and distributed across quantum harmonic oscillators.
  • Estimator variance is quantized and equals oscillator energy levels, with minimum variance at minimum energy.
  • Quantum harmonic oscillators achieve the Cramér-Rao lower bound at the lowest energy level.
  • The collective mode's probability density function at the lowest energy matches the posterior probability distribution.

Conclusions:

  • The physical world can be decomposed into informational elements represented by quantum harmonic oscillators.
  • The square modulus of the collective mode at the lowest energy signifies the most probable reality.
  • This supports the view that the universe is fundamentally composed of informational, not physical, parts.