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Justifying Born's Rule P = |Ψ|2 Using Deterministic Chaos, Decoherence, and the de Broglie-Bohm Quantum Theory
1Institut NEEL, CNRS and Université Grenoble Alpes, F-38000 Grenoble, France.
Entropy (Basel, Switzerland)
|November 27, 2021
Summary
This study derives Born's rule from pilot-wave theory using a toy model. Entanglement and chaos rapidly relax particle distributions to the Born probability law, akin to Boltzmann's kinetic theory.
Area of Science:
- Quantum mechanics
- Foundations of physics
- Statistical mechanics
Background:
- Pilot-wave theory offers an alternative to standard quantum mechanics.
- Born's rule is a fundamental postulate in quantum mechanics.
- Understanding the origin of quantum probabilities is a key challenge.
Purpose of the Study:
- To derive Born's rule from the de Broglie-Bohm pilot-wave theory.
- To investigate the role of entanglement and chaos in quantum probability emergence.
- To connect pilot-wave theory with classical statistical mechanics.
Main Methods:
- Development of a toy model with a particle and an environment of Bohmian pointers (qubits).
- Analysis of particle-environment entanglement and deterministic chaos.
- Application of concepts from Boltzmann's kinetic theory.
Main Results:
- Demonstration of rapid relaxation from arbitrary statistical distributions to the Born rule |Ψ(x)|².
- Establishment of a quantum equilibrium regime through entanglement and chaos.
- Exhibition of an H-theorem analogue for the relaxation process.
Conclusions:
- Born's rule can be derived from pilot-wave theory under specific conditions.
- Entanglement and deterministic chaos are crucial for the emergence of quantum probabilities.
- The study provides a novel perspective linking quantum foundations with kinetic theory.
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