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arxiv: 2409.01294 · v1 · submitted 2024-09-02 · 🪐 quant-ph · gr-qc· hep-th

De Broglie-Bohm Quantum Mechanics

Antony Valentini This is my paper

Pith reviewed 2026-05-23 21:14 UTC · model grok-4.3

classification 🪐 quant-ph gr-qchep-th
keywords de Broglie-Bohmpilot-wave theoryquantum field theorycosmologygravitationhidden variablesdeterministic quantum mechanics
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The pith

The de Broglie-Bohm pilot-wave formulation extends consistently to field theory, high-energy physics, gravitation, and cosmology.

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

The paper gives an overview of the de Broglie-Bohm pilot-wave approach to quantum mechanics. It argues that this formulation, which supplements the wave function with actual particle trajectories guided by the wave, can be carried over to relativistic field theories and gravitational settings. A reader would care because the approach supplies deterministic trajectories where standard quantum theory supplies only probabilities, potentially clarifying dynamics in regimes where quantum effects meet gravity or high energies. The review collects existing results that demonstrate these extensions remain consistent with the original non-relativistic theory.

Core claim

The de Broglie-Bohm pilot-wave formulation of quantum mechanics admits consistent extensions to quantum field theory, high-energy physics, gravitation, and cosmology, supplying deterministic particle or field trajectories in each case.

What carries the argument

The pilot-wave guidance equation that determines actual trajectories from the wave function.

If this is right

  • Field operators in quantum field theory acquire definite values along trajectories.
  • Cosmological models gain explicit field trajectories that evolve deterministically from initial conditions.
  • Gravitational interactions can be treated by coupling the pilot wave to a metric without altering the guidance law.
  • High-energy scattering processes receive a causal description via trajectory ensembles.
  • The measurement problem receives the same resolution in these extended domains as in ordinary quantum mechanics.

Where Pith is reading between the lines

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

  • If the extensions hold, the same initial-condition problem that exists in non-relativistic de Broglie-Bohm theory would also limit predictive power in cosmology.
  • The framework could be tested by checking whether predicted trajectory statistics in analogue gravity systems match standard quantum predictions.
  • Extensions to quantum gravity might require choosing a preferred foliation, which would then need observational consequences distinct from other quantum-gravity approaches.

Load-bearing premise

The de Broglie-Bohm approach admits consistent relativistic and gravitational extensions without introducing new inconsistencies not already present in standard quantum field theory.

What would settle it

Discovery of an inconsistency or non-local signaling effect in a relativistic pilot-wave field theory that cannot be removed by the same regularization techniques used in standard quantum field theory.

Figures

Figures reproduced from arXiv: 2409.01294 by Antony Valentini.

Figure 1
Figure 1. Figure 1: Quantum relaxation for a two-dimensional oscillator (Abra [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Approximate exponential decay of H¯ (t) for a two-dimensional oscil￾lator (Abraham, Colin, and Valentini 2014). The error is estimated by running simulations with different grids (solid curves). The dashed curve shows a best fit to an exponential function a exp[−b(t/2π)] + c. 1992; D¨urr and Teufel 2009). However, this approach is conceptually circular: the Born rule is assumed at t = 0 in order to derive … view at source ↗
read the original abstract

We provide an overview of the de Broglie-Bohm pilot-wave formulation of quantum mechanics, emphasising its applications to field theory, high-energy physics, gravitation, and cosmology.

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 / 0 minor

Summary. The manuscript provides an overview of the de Broglie-Bohm pilot-wave formulation of quantum mechanics, emphasising its applications to field theory, high-energy physics, gravitation, and cosmology.

Significance. As a review paper, the work synthesizes existing literature on the de Broglie-Bohm approach rather than advancing new derivations or theorems. If the coverage is balanced and accurate, it could serve as a useful reference point for researchers exploring extensions of pilot-wave ideas beyond non-relativistic quantum mechanics.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive summary, significance assessment, and recommendation to accept the manuscript. There are no major comments requiring response.

Circularity Check

0 steps flagged

No significant circularity: review paper with no derivation chain

full rationale

This is an overview/review paper whose abstract and structure explicitly frame it as a summary of existing literature on de Broglie-Bohm theory and its extensions to field theory, HEP, gravitation, and cosmology. No new predictions, first-principles derivations, fitted parameters, or uniqueness theorems are advanced in the provided abstract or described content. The central claim is descriptive of published work rather than a novel assertion whose validity reduces to self-citation or input data. No load-bearing steps exist that could exhibit self-definitional, fitted-input, or self-citation circularity. The paper is therefore self-contained as a survey against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no free parameters, axioms, or invented entities can be identified from the provided text.

pith-pipeline@v0.9.0 · 5528 in / 886 out tokens · 18054 ms · 2026-05-23T21:14:57.610847+00:00 · methodology

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

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extends
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Reference graph

Works this paper leans on

8 extracted references · 8 canonical work pages · 2 internal anchors

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    Colin, S. (2012). Relaxation to quantum equilibrium for Dirac fermions in the de Broglie-Bohm pilot-wave theory. Proceedings of the Royal Society A 468, 1116–1135. Colin, S. and Struyve, W. (2007). A Dirac sea pilot-wave model for q uantum field theory. Journal of Physics A 40, 7309–7341. Colin, S. and Valentini, A. (2013). Mechanism for the suppression of...

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    K., Namgung, W., Soh, K

    Kim, S. K., Namgung, W., Soh, K. S., and Yee, J. H. (1990). Equivalenc e between the Weyl, Coulomb, and unitary gauges in the functional Sc hr¨ odinger picture. Physical Review D 41, 3792–3795. Kosteleck´ y, V. A. and Mewes, M. (2002). Signals for Lorentz viola tion in electrodynamics. Physical Review D 66, 056005. Kuchaˇ r, K. V. (2011). Time and interpr...

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    Black Holes, Information Loss, and Hidden Variables

    Pinto-Neto, N. and Fabris, J. C. (2013). Quantum cosmology from the de Broglie–Bohm perspective. Classical and Quantum Gravity 30, 143001. Pinto-Neto, N. and Sergio Santini, E. (2002). The consistency of c ausal quantum geometrodynamics and quantum field theory. General Relativity and Gravitation 34, 505–532. Roser, P. and Valentini, A. (2014). Classical a...

    work page internal anchor Pith review Pith/arXiv arXiv 2013

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    Valentini, A. (2025). Introduction to quantum foundations and pilot-wave theory. Oxford: Oxford University Press. Valentini, A. and Westman, H. (2005). Dynamical origin of quantum p rob- abilities. Proceedings of the Royal Society A 461, 253–272. Vigier, J. P. (1985). Nonlocal quantum potential interpretation o f relativistic actions at a distance in many...

    work page 2025