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Stein's method, many interacting worlds and quantum mechanics

I. McKeague,E. Pekoz,Yvik Swan

Published 2016 in arXiv: Probability

ABSTRACT

Hall, Deckert and Wiseman (2014) recently proposed that quantum theory can be understood as the continuum limit of a deterministic theory in which there is a large, but finite, number of classical "worlds." A resulting Gaussian limit theorem for particle positions in the ground state, agreeing with quantum theory, was conjectured in Hall, Deckert and Wiseman (2014) and proven by McKeague and Levin (2016) using Stein's method. In this article we propose new connections between Stein's method and Many Interacting Worlds (MIW) theory. In particular, we show that quantum position probability densities for higher energy levels beyond the ground state arise as distributional fixed points in a new generalization of Stein's method. These are then used to obtain a rate of distributional convergence for conjectured particle positions in the first energy level above the ground state to the (two-sided) Maxwell distribution; new techniques must be developed for this setting where the usual "density approach" Stein solution (see Chatterjee and Shao (2011)) has a singularity.

PUBLICATION RECORD

  • Publication year

    2016

  • Venue

    arXiv: Probability

  • Publication date

    2016-06-21

  • Fields of study

    Mathematics, Physics

  • Identifiers
    arXiv 1606.06618
  • External record

    Open on Semantic Scholar

  • Source metadata

    Semantic Scholar

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