Deriving Quantum Formalism from Information Limits in Microscopic Systems

Abstract: While the standard postulates of quantum mechanics successfully predict a wide range of phenomena, their physical underpinnings remain elusive. In this presentation, I derive the standard formalism of quantum theory—Born’s rule, Hilbert space formalism, and Schrödinger equation—from the limitations of information accessibility in microscopic systems. I demonstrate that information-theoretic constraints imposed on microscopic systems with a single variable lead directly to their inherent probabilistic behavior under different measurement scenarios. This limitation, combined with the conservation of probability, is utilized to derive Born's probability rule, the Hilbert space formalism, and ultimately, the Schrödinger equation governing the dynamics of these systems. Furthermore, I establish a connection between these single-variable systems and traditional quantum systems. I show that coherence, essential for observing quantum phenomena, restricts the number of independent variables in a coherent beam to just one, thereby supporting the connection between our framework and established quantum phenomena. This work suggests that quantum phenomena may emerge from the fundamental limitations of information accessibility. It offers a new perspective on the foundations of quantum theory and opens new avenues for further exploration.

mathematical physicsgeneral physicsquantum physics

Audience: advanced learners

( paper )

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QM Foundations & Nature of Time seminar

Series comments: Description: Physics foundations discussion seminar

Current access link in th.if.uj.edu.pl/~dudaj/QMFNoT

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