Ground states in the Many Interacting Worlds approach

Herrmann, H.; Hall, Michael J. W.; Wiseman, Howard M.; André, Deckert, Dirk -

doi:10.48550/arxiv.1712.01918

Cited by 7 publications

(9 citation statements)

References 19 publications

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“…There are some similarities between the present model and the work of Madelung [12], and also various works on many-interactingworlds [13,14,15,16,17,18] for single quantum particles. However, this is really a mathematical framework for the local Schrödinger picture of the Parallel Lives interpretation of quantum mechanics [19,20], and should be consistent with the local Heisenberg picture frameworks that have been developed elsewhere [21,22,23,24,25,26,27,28,29,30,31].…”

Section: Introductionsupporting

confidence: 54%

Local Quantum Theory with Fluids in Space-Time

Waegell¹

2021

Preprint

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A local theory of relativistic quantum physics in space-time, which makes all of the same empirical predictions as the conventional delocalized theory in configuration space, is presented and interpreted. Each physical system is characterized by a set of indexed piece-wise single-particle wavefunctions in space-time, each with with its own coefficient, and these wavefields replace entangled states in higherdimensional spaces. Each wavefunction of a fundamental system describes the motion of a portion of a conserved fluid in space-time, with the fluid decomposing into many classical point particles, each following a world-line and recording a local memory. Local interactions between two systems take the form of local boundary conditions between the differently indexed pieces of those systems' wave-fields, with new indexes encoding each orthogonal outcome of the interaction. The general machinery is introduced, including the local mechanisms for entanglement and interference. The experience of collapse, Born rule probability, and environmental decoherence are discussed. A number of illustrative examples are given, including a Von Neumann measurement, and a test of Bell's theorem.

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Section: Introductionsupporting

confidence: 54%

Local Quantum Theory with Fluids in Space-Time

Waegell¹

2021

Preprint

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“…In addition, our simulations were restricted to one particle in 1D. The MIW approach has been successfully used to simulate one particle in 2D (or, equivalently, two particles in 1D) [38,42] and 3D [42], but only to find the ground state configuration. Combining these research directions to be able to simulate stable excited states for two particles in 1D, and beyond, is a challenge for future work.…”

Section: Discussionmentioning

confidence: 99%

“…Recently, we have generalised MIW for a 2D particle, which is equivalent to two 1D particles, with some numerical success [38]. However, that study was restricted to finding ground states-stationary states with no nodes in the wavefunction.…”

Section: Simulationsmentioning

confidence: 99%

Nonlocality in Bell’s Theorem, in Bohm’s Theory, and in Many Interacting Worlds Theorising

Ghadimi

Hall

Wiseman

2018

Entropy

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Locality" is a fraught word, even within the restricted context of Bell's theorem. As one of us has argued elsewhere, that is partly because Bell himself used the word with different meanings at different stages in his career. The original, weaker, meaning for locality was in his 1964 theorem: that the choice of setting by one party could never affect the outcome of a measurement performed by a distant second party. The epitome of a quantum theory violating this weak notion of locality (and hence exhibiting a strong form of nonlocality) is Bohmian mechanics. Recently, a new approach to quantum mechanics, inspired by Bohmian mechanics, has been proposed: Many Interacting Worlds. While it is conceptually clear how the interaction between worlds can enable this strong nonlocality, technical problems in the theory have thus far prevented a proof by simulation.Here we report significant progress in tackling one of the most basic difficulties that needs to be overcome: correctly modelling wavefunctions with nodes.

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“…In this article we study the question of how the MIW approach can be extended to general d-dimensional settings. Herrmann et al [10] examined the case d = 2 and proposed using Delaunay triangulations and Voronoi tesselations of point configurations to extend the notion of the interworld potential. They developed a numerical algorithm to estimate the resulting ground state configuration, but the question of whether it is possible to establish an asymptotically valid approximation of such a solution to the classical quantum harmonic oscillator ground state solution was not addressed.…”

Section: Introductionmentioning

confidence: 99%

Stein’s method and approximating the quantum harmonic oscillator

McKeague¹,

Peköz²,

Swan³

2019

Bernoulli

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Hall et al. (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 et al. (2014) and proven by McKeague and Levin (2016) using Stein’s method. In this article we show how quantum position probability densities for higher energy levels beyond the ground state may 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.

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Ground states in the Many Interacting Worlds approach

Cited by 7 publications

References 19 publications

Local Quantum Theory with Fluids in Space-Time

Local Quantum Theory with Fluids in Space-Time

Nonlocality in Bell’s Theorem, in Bohm’s Theory, and in Many Interacting Worlds Theorising

Stein’s method and approximating the quantum harmonic oscillator

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