Unified Quantum Dynamics: The Emergence of the Born Rule

• URL: http://arxiv.org/abs/2504.06495v1
• Date: Tue, 08 Apr 2025 23:43:16 GMT
• Title: Unified Quantum Dynamics: The Emergence of the Born Rule
• Authors: Martin Weidner,
• Abstract summary: We show that the Born rule emerges naturally from a modified Schr"odinger equation that includes "small-signal truncation"<n>This parallels the way quantum decoherence gives rise to the branches of the multiverse in the "Many-Worlds Interpretation"
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: While the Born rule is traditionally introduced as a separate postulate of quantum mechanics, we show it emerges naturally from a modified Schr\"odinger equation that includes "small-signal truncation". This parallels the way quantum decoherence gives rise to the branches of the multiverse in the "Many-Worlds Interpretation", eliminating the need for a separate measurement postulate. Our approach thus offers a unified framework in which both the emergence of multiple branches of the multiverse and their statistical properties follow from a single fundamental law of motion. We model "small-signal truncation" in a somewhat stylized manner, but we argue that the precise details of its underlying physical mechanism do not affect the emergence of the Born rule.

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