Quantum Theory from Probability Conservation

Shaghaghi, Mehran (2024) Quantum Theory from Probability Conservation. [Preprint]

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Official URL: https://www.researchgate.net/publication/384534486...

Abstract

We present a first-principles derivation of the standard formalism of quantum theory through an information-theoretic analysis of single-variable physical systems –systems characterized by only one independent variable. These systems, with a minimal information capacity of exactly one bit, exhibit inherently indeterministic behavior under independent measurements while permitting probabilistic descriptions for dependent measurements. By enforcing probability conservation in the transformations of outcome probabilities across different measurement scenarios, we derive the core components of standard quantum theory, including the Born rule, the Hilbert space structure, and the Schrödinger equation. Furthermore, we demonstrate that the experimental requirements for observing quantum phenomena –specifically, preparing physical systems in coherent states under strict conditions, such as ultralow temperatures or high fields– effectively constrain the number of independent variables to one, thereby enforcing single-variable behavior. This first-principles, information-theoretic derivation establishes that quantum theory fundamentally describes the physics of single-variable systems and provides a concrete realization of Wheeler’s “it from bit” idea.

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