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First Principles Numerical Demonstration of Emergent Decoherent Histories

Philipp Strasberg, Teresa E. Reinhard, and Joseph Schindler

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Phys. Rev. X 14, 041027 – Published 30 October, 2024

DOI: https://doi.org/10.1103/PhysRevX.14.041027

Abstract

Within the histories formalism the decoherence functional is a formal tool to investigate the emergence of classicality in isolated quantum systems, yet an explicit evaluation of it from first principles has not been reported. We provide such an evaluation for up to five-time histories based on exact numerical diagonalization of the Schrödinger equation. We find a robust emergence of decoherence for slow and coarse observables of a generic random matrix model and extract a finite-size scaling law by varying the Hilbert space dimension over 4 orders of magnitude. Specifically, we conjecture and observe an exponential suppression of coherent effects as a function of the particle number of the system. This suggests a solution to the preferred basis problem of the many-worlds interpretation (or the set selection problem of the histories formalism) within a minimal theoretical framework without relying on environmentally induced decoherence, quantum Darwinism, Markov approximations, low-entropy initial states, or ensemble averages.

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Can Classical Worlds Emerge from Parallel Quantum Universes?

Published 30 October, 2024

Simulations deliver hints on how the multiverse produced according to the many-worlds interpretation of quantum mechanics might be compatible with our stable, classical Universe.

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Popular Summary

The interpretation of quantum mechanics is not a purely metaphysical question but has profound consequences for how we view the world and for what kind of “theory of everything” we are looking for. Each interpretation has very different consequences. The many-worlds interpretation, for example, predicts the existence of multiple parallel universes existing at the same spacetime location in a “multiverse.” The existential question of this interpretation is whether the multiverse is compatible with our perception of a single, classical universe. In the first extensive numerical investigation of this question, relying on nothing but the standard framework of quantum mechanics, we find that it is.

To this end, we introduce two rigorous quantifiers to measure the loss of quantum features, in the form of interference effects, between different universes of the multiverse. We find that these quantifiers are exponentially small as a function of the particle number of the system. Since objects of daily life contain a huge number of particles, this explains why the multiverse is not directly perceptible to us.

Our theoretical framework combines tools from statistical mechanics and the decoherent histories framework of quantum mechanics. By exactly solving the Schrödinger equation, we find that classicality emerges in a genuine isolated quantum system, and we further reveal that it is a ubiquitous phenomenon not requiring any fine-tuning of the initial state.

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Phys. Rev. X 14, 041027– Published 30 October, 2024
  • Received 11 May 2023
  • Revised 1 July 2024
  • Accepted 30 July 2024
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