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arxiv: 1907.00258 · v1 · pith:MKO5OQDDnew · submitted 2019-06-29 · 🌀 gr-qc · quant-ph

On the Quantum-to-Classical Transition of Primordial Perturbations

Wouter Ryssens This is my paper

Pith reviewed 2026-05-25 12:33 UTC · model grok-4.3

classification 🌀 gr-qc quant-ph
keywords pilot-wave theoryprimordial perturbationsinflationquantum-to-classical transitioncosmic microwave backgrounddecoherencesqueezingasymmetry
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The pith

Pilot-wave theory accounts for the quantum-to-classical transition of primordial perturbations and the emergence of asymmetry from an initially symmetric state.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The dissertation examines how quantum fluctuations in the early universe become the classical inhomogeneities seen in galaxies and the cosmic microwave background, and how asymmetry arises despite an initially symmetric state. Standard approaches such as squeezing and decoherence are reviewed but found to have limitations in fully addressing both issues. The pilot-wave approach is then applied to scalar perturbations in slow-roll inflation, with numerical trajectories shown to reach the classical limit while generating the required asymmetry. This supplies a single framework that resolves the two questions without additional mechanisms.

Core claim

When the pilot-wave formalism is applied to quantized scalar perturbations around the slow-roll inflation background, the resulting trajectories approach classical evolution and simultaneously produce asymmetry from symmetric initial conditions, as demonstrated directly by the numerical results.

What carries the argument

Pilot-wave trajectories for the perturbation modes, evolved via the guidance equation and shown numerically to recover classical behavior.

If this is right

  • The observed large-scale homogeneity together with small-scale structure follows directly from the quantum initial state through deterministic pilot-wave dynamics.
  • Asymmetry in the current universe is generated by the pilot-wave evolution itself rather than by an external symmetry-breaking process.
  • The limitations identified in squeezing and decoherence indicate that those mechanisms alone do not suffice to explain the classical appearance of perturbations.
  • Cosmic microwave background measurements can be reinterpreted as outcomes of these specific classical trajectories.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same numerical trajectory method could be extended to tensor modes to check consistency with gravitational wave predictions.
  • If the pilot-wave picture holds, it offers a deterministic alternative to standard decoherence accounts that could be compared against future precision CMB data on non-Gaussianity.

Load-bearing premise

The pilot-wave formalism applies consistently to the quantized scalar perturbations in the slow-roll inflation background without further modifications that would alter the claimed resolution of the transition and asymmetry questions.

What would settle it

A numerical simulation of the pilot-wave trajectories for the scalar perturbations that fails to approach classical evolution or fails to generate asymmetry from symmetric initial conditions.

Figures

Figures reproduced from arXiv: 1907.00258 by Wouter Ryssens.

Figure 0
Figure 0. Figure 0 [PITH_FULL_IMAGE:figures/full_fig_p006_0.png] view at source ↗
Figure 9.1
Figure 9.1. Figure 9.1: Superposition of quantum numbers [1, 6, 9] with weights of equal amplitude but random phase. Parameters used were H = 0.01, k = 1 and q(ηini) = 1 for de Sitter inflation [PITH_FULL_IMAGE:figures/full_fig_p084_9_1.png] view at source ↗
Figure 9
Figure 9. Figure 9 [PITH_FULL_IMAGE:figures/full_fig_p084_9.png] view at source ↗
Figure 9
Figure 9. Figure 9: fig. 9.4 for a simple superposition. A log-log version of this plot is shown in fig. 9.5, together with a [PITH_FULL_IMAGE:figures/full_fig_p086_9.png] view at source ↗
Figure 9
Figure 9. Figure 9 [PITH_FULL_IMAGE:figures/full_fig_p089_9.png] view at source ↗
read the original abstract

Detailed measurements of the cosmic microwave background indicate the large-scale homogeneity of the universe. On very small scales, we observe however inhomogeneities such as galaxies, stars, planets and ourselves. In the context of hot Big-Bang cosmology, these inhomogeneities are often explained as the remains of quantum fluctuations at very early times, enlarged to observable scales through the process of inflation. In this dissertation, I examine two important questions surrounding this scenario: a) How do inherently quantal fluctuations transition to the observed inhomogeneities, which behave classically? ; and b) If the initial state of the universe was symmetric, how can the currently observed state? This dissertation is organized in three parts. Part one first introduces the slow-roll inflation model and then discusses the behavior of small (scalar) perturbations to this model. The second part investigates various answers provided to the questions above, starting with some general observations on the classical limit of quantum mechanics with special attention given to the inverted harmonic oscillator. The formalisms of `squeezing' and decoherence are discussed and weak points are pointed out. In the final part, I examine in detail the pilot-wave approach to the problem, discussing in detail the classical limit of the theory and how pilot-wave theory addresses both questions above. Numerical results for pilot-wave trajectories are presented, illustrating directly the classical limit.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The dissertation examines the quantum-to-classical transition of primordial scalar perturbations in slow-roll inflation and the emergence of observed asymmetry from an initially symmetric state. After reviewing the inflationary background and Mukhanov-Sasaki perturbations, it critiques squeezing and decoherence approaches, then develops the pilot-wave (de Broglie-Bohm) treatment by applying the guidance equation to the quantized perturbations and presenting numerical integrations of trajectories that are claimed to exhibit the classical limit while breaking symmetry.

Significance. If the numerical trajectory results hold, the work supplies a direct, non-probabilistic illustration of how pilot-wave dynamics can produce classical inhomogeneities and select a preferred direction from symmetric initial conditions, offering a concrete alternative to standard decoherence arguments in quantum cosmology. The explicit numerical evidence for the classical limit is a positive feature of the exploratory study.

minor comments (3)
  1. The abstract and part-three description refer to 'numerical results for pilot-wave trajectories' but the manuscript should include a dedicated subsection (e.g., §X.Y) specifying the integration method, initial conditions for the Mukhanov-Sasaki field, and quantitative measures (e.g., variance growth or Wigner-function narrowing) used to demonstrate the classical limit.
  2. Notation for the guidance equation applied to the Mukhanov-Sasaki variable should be introduced with an explicit equation number in the pilot-wave section, together with a brief statement of the background slow-roll metric and mode expansion to ensure the construction is self-contained.
  3. The discussion of weak points in squeezing and decoherence formalisms would benefit from one or two concrete counter-examples or references to specific equations in the literature that the pilot-wave approach is said to avoid.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful reading and positive assessment of the dissertation, particularly the recognition that the numerical trajectory results provide a direct illustration of the classical limit in the pilot-wave approach. We note the recommendation for minor revision. No specific major comments were listed in the report, so we have no point-by-point responses below. Any minor issues identified during revision will be addressed.

Circularity Check

0 steps flagged

No significant circularity; derivation applies standard pilot-wave formalism to standard inflationary perturbations

full rationale

The dissertation applies the de Broglie-Bohm guidance equation in its standard form to the Mukhanov-Sasaki variable on a slow-roll background. Central claims rest on direct numerical integration of trajectories, which constitute independent computational output rather than a fit or self-referential definition. No step equates a derived quantity to an input parameter by construction, renames a known result, or loads the argument on a self-citation whose content is itself unverified. The work is explicitly exploratory and presents the numerical illustrations as direct evidence of the classical limit, keeping the derivation self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract alone supplies insufficient detail to enumerate specific free parameters, axioms, or invented entities; the work relies on standard assumptions of slow-roll inflation and the pilot-wave interpretation without introducing new entities.

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Reference graph

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