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arXiv · 2504.06495

Unified Quantum Dynamics: The Emergence of the Born Rule

Martin Weidner
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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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Martin Weidner. 2025-04-08. Unified Quantum Dynamics: The Emergence of the Born Rule. https://arxiv.org/abs/2504.06495

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