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Quantum mechanics in configuration space in context

T0 review · 2 major / 1 minor · reviewed 2026-06-27 · grok-4.3

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Pith's one-line read Quantum mechanics in configuration space avoids the momentum definition inconsistency that appears in canonical quantisation by using a direct quantisation of Newtonian mechanics.

desk verdict This is a discussion paper that situates the authors' 2025 configuration-space formalism but introduces no new technical results or checks. read the letter →

arxiv 2606.17622 v1 pith:ADCR3GF2 submitted 2026-06-16 quant-ph

Arwa Bukhari , Margherita Moro , Max Davies , Alastair Wilson , Almut Beige This is my paper · ORCID
classification quant-ph
keywords quantummechanicsconfigurationspacecanonicalquantisationNewtonianposition-velocitystateswave-particledualitymomentuminconsistency
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper places a recently introduced formalism into context by showing that it rests on a physically motivated quantisation of Newtonian mechanics rather than on canonical quantisation. In this approach, classical position-velocity states (x,v) are promoted to pairwise distinguishable quantum states |x,v> that serve as the basis for the Hilbert space and evolve exactly along classical trajectories. A sympathetic reader would care because the construction removes a conceptual mismatch between the way momentum is defined in standard quantum mechanics and the way it behaves in classical mechanics. The paper also notes that the two formalisms therefore originate from two distinct classical starting points, one Lagrangian and one Newtonian.

What carries the argument

The |x,v> states obtained by promoting classical position-velocity pairs to pairwise distinguishable quantum states that evolve along classical trajectories.

What would settle it

A calculation or measurement showing that the |x,v> states produce observable predictions that differ from standard quantum mechanics in a regime where both formalisms can be applied without additional assumptions.

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Extended reading notes

Core claim

Quantum mechanics in configuration space increases the continuity between quantum and classical mechanics by avoiding a conceptual inconsistency associated with the definition of momentum in canonical quantisation. The formalism promotes classical position-velocity states (x,v) to pairwise distinguishable quantum states |x,v> that form the basis of the Hilbert space of individual particles and evolve along classical trajectories. Standard quantum mechanics and quantum mechanics in configuration space are based on two distinct formulations of classical mechanics.

Load-bearing premise

Promoting classical position-velocity states to pairwise distinguishable quantum states that evolve along classical trajectories yields a physically consistent theory that introduces no new inconsistencies and does not contradict established quantum predictions.

Editorial extensions

If this is right

  • The new formalism supplies an alternative route for modelling a mechanical particle in free space that stays closer to Newtonian trajectories.
  • Wave-particle duality is implemented through the pairwise distinguishability of the |x,v> states rather than through operator promotion.
  • Any conceptual tension arising from the momentum operator in canonical quantisation is sidestepped because momentum is never promoted from a classical function in the same way.
  • The two quantum theories remain empirically equivalent for the cases examined while resting on different classical foundations.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the assumption holds, the formalism could be extended to interacting particles by defining suitable joint |x,v> states without invoking interaction Hamiltonians at the quantisation step.
  • The distinction between the two classical starting points suggests that other classical formulations, such as Hamilton-Jacobi theory, might yield still further quantisation routes with different continuity properties.
  • Experimental tests could focus on whether the strict classical evolution of |x,v> states survives when the system is coupled to a measuring apparatus.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 1 minor

Summary. The manuscript claims that quantum mechanics in configuration space, as introduced in Bukhari et al. (New J. Phys. 27, 084501, 2025), quantizes Newtonian mechanics by promoting classical (x,v) states to pairwise distinguishable |x,v> states that evolve along classical trajectories. This formalism is argued to increase continuity with classical mechanics by avoiding a conceptual inconsistency in the momentum definition inherent to canonical quantization. The paper further states that standard quantum mechanics and this configuration-space approach rest on distinct formulations of classical mechanics, with the discussion centered on modeling a free particle.

Significance. If the formalism proves internally consistent and capable of reproducing established quantum predictions, the work could provide a useful conceptual bridge between classical and quantum descriptions, clarifying wave-particle duality through a physically motivated quantization procedure. The paper's emphasis on distinct classical foundations is a clear framing contribution, though its significance remains conditional on independent verification of physical viability beyond the referenced prior construction.

major comments (2)
  1. [Modelling of a mechanical particle in free space] Modelling of a mechanical particle in free space: The evolution of |x,v> states along strictly classical trajectories is presented without a derivation or explicit argument showing how superpositions encode interference, diffraction, or the uncertainty principle, which is load-bearing for the claim that the formalism constitutes a physically consistent alternative to canonical quantization.
  2. [Introduction] The avoidance of the momentum inconsistency is defined relative to the 2025 Bukhari et al. construction without an independent external benchmark or cross-check against standard QM predictions shown in this manuscript, leaving the central continuity claim dependent on the prior work's internal definitions.
minor comments (1)
  1. The abstract and introduction could more explicitly delineate the novel contextual contributions of this paper from the foundational results of the 2025 reference.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive report. The manuscript is a contextual discussion building directly on Bukhari et al. (2025), and we address the two major comments below by clarifying scope and offering targeted revisions where they strengthen presentation without expanding beyond the paper's stated purpose.

read point-by-point responses

  1. Referee: [Modelling of a mechanical particle in free space] Modelling of a mechanical particle in free space: The evolution of |x,v> states along strictly classical trajectories is presented without a derivation or explicit argument showing how superpositions encode interference, diffraction, or the uncertainty principle, which is load-bearing for the claim that the formalism constitutes a physically consistent alternative to canonical quantization.

    Authors: The manuscript's scope is contextual framing of the free-particle case rather than a self-contained re-derivation of the full formalism. The explicit construction showing how |x,v> superpositions encode interference, diffraction, and uncertainty is given in Bukhari et al. (New J. Phys. 27, 084501, 2025), which this paper cites as its foundation. To improve accessibility we will add a short paragraph in the modelling section that summarizes the key superposition argument from the prior work, including a concrete free-particle example of interference, while keeping the focus on continuity and classical foundations. revision: partial

  2. Referee: [Introduction] The avoidance of the momentum inconsistency is defined relative to the 2025 Bukhari et al. construction without an independent external benchmark or cross-check against standard QM predictions shown in this manuscript, leaving the central continuity claim dependent on the prior work's internal definitions.

    Authors: This is correct: the continuity claim is framed relative to the Bukhari et al. (2025) definitions because the present paper's contribution is to place that formalism in context and to highlight that standard QM and configuration-space QM rest on distinct classical starting points (Newtonian vs. Hamiltonian). No new predictive cross-checks are performed here precisely because the manuscript is not a validation study. We will revise the introduction to state this reliance and the paper's distinct conceptual contribution more explicitly. revision: yes

Circularity Check

1 steps flagged · score 6.0 of 10

Core claim of inconsistency avoidance relies on self-cited 2025 formalism

  1. self citation load bearing [Abstract]
    "Bukhari et al. [New J. Phys. 27, 084501 (2025)] recently introduced an alternative approach to quantum mechanics, namely quantum mechanics in configuration space. This formalism is based on a physically motivated quantisation of Newtonian mechanics and promotes the classical position-velocity states (x,v) to pairwise distinguishable quantum states. The resulting |x,v> states form the basis of the Hilbert space of individual quantum mechanical particles and evolve along classical trajectories."

    The claim that the formalism 'increases the continuity between quantum and classical mechanics by avoiding a conceptual inconsistency' is defined relative to the 2025 construction by the same lead author; the present paper supplies no new equations or external validation showing how |x,v> states reproduce QM predictions while evading the inconsistency.

full rationale

The paper's central demonstration that the configuration-space formalism increases continuity with classical mechanics by avoiding a momentum-definition inconsistency rests on the |x,v> construction introduced in the cited 2025 work by the lead author. No independent derivation or external benchmark is supplied in the present text; the context paper essentially restates and interprets the prior self-authored result. This matches self_citation_load_bearing with partial circularity (score 6) because the load-bearing premise reduces to the unverified prior construction while the paper still adds contextual discussion of distinct classical formulations.

Assumptions & free parameters 0 free parameters · 0 assumptions · 0 invented entities

Abstract-only; no explicit free parameters, axioms, or invented entities are stated or derivable from the provided text.

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Cite this review

Pith. "Pith review of Quantum mechanics in configuration space in context." pith.science (2026). https://pith.science/paper/ADCR3GF2

@misc{pith2026260617622,
  author       = {Pith},
  title        = {Pith review of: Quantum mechanics in configuration space in context},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ADCR3GF2}},
  note         = {Machine review of arXiv:2606.17622}
}
read the original abstract

To enhance the way in which wave-particle duality is implemented in the modelling of quantum mechanical systems, Bukhari et al. [New J. Phys. 27, 084501 (2025)] recently introduced an alternative approach to quantum mechanics, namely quantum mechanics in configuration space. This formalism is based on a physically motivated quantisation of Newtonian mechanics and promotes the classical position-velocity states (x,v) to pairwise distinguishable quantum states. The resulting |x,v> states form the basis of the Hilbert space of individual quantum mechanical particles and evolve along classical trajectories. In this paper, we consider the modelling of a mechanical particle in free space and put quantum mechanics in configuration space into context. It is shown that this formalism increases the continuity between quantum and classical mechanics by avoiding a conceptual inconsistency associated with the definition of momentum in canonical quantisation. In addition, we emphasise that standard quantum mechanics and quantum mechanics in configuration space are based on two distinct formulations of classical mechanics.

Figures

Figures reproduced from arXiv: 2606.17622 by the authors.

Figure 1
Figure 1. FIG. 1. Illustration of the relations between the three main [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Illustration of four different sets of basis states which [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. An illustration of how QMCS and SQM relate to [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

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Reference graph

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