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arxiv: 2604.15130 · v1 · submitted 2026-04-16 · 🌀 gr-qc

On measuring the Quantum Universe

David Vasak , Johannes Kirsch , Juergen Struckmeier This is my paper

Pith reviewed 2026-05-10 10:27 UTC · model grok-4.3

classification 🌀 gr-qc
keywords quantum cosmologyWheeler-DeWitt equationtorsion gravityFLRW universeweak measurementde Broglie-Bohmthird quantizationcosmic time
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The pith

The wave function of the universe is a superposition of eigenfunctions of a nonzero quantum Hamiltonian, with cosmic time conjugate to spatial curvatures.

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

The paper analyzes the Wheeler-DeWitt approach to quantum cosmology when extended to theories with torsion. It treats the FLRW universe dynamics as a classical Hamiltonian system of point particle mechanics. Because the Hamiltonian is not zero, third quantization does not force cosmic time to vanish. The universal wave function becomes a superposition of eigenfunctions with cosmic time as the conjugate variable to the eigenvalues given by spatial curvatures. Weak measurements are introduced to measure parameters of matter and spacetime without collapsing the total wave function, and the de Broglie-Bohm interpretation is used to handle the effective wave function and boundary conditions.

Core claim

We present a theoretical analysis of the WDW approach to quantum cosmology extended to gravity theories with torsion. The dynamics of the FLRW universe is formulated as a classical Hamiltonian problem of point particle mechanics. Unlike in the WDW formalism, the Hamiltonian is not zero, though, and the 3rd quantization does not enforce the cosmic time to vanish. The wave function of the Universe appears as a superposition of eigenfunctions of the quantum Hamiltonian with the cosmic time being the conjugate to its eigenvalues, spatial curvatures. The notion of weak measurement is then introduced to avoid the collapse of the total universal wave function upon measurements of the parameter set

What carries the argument

Torsion-extended Hamiltonian for the FLRW universe treated as point particle mechanics, which remains nonzero after third quantization and lets cosmic time serve as conjugate to spatial curvature eigenvalues.

Load-bearing premise

The third quantization of the torsion-extended Hamiltonian does not force cosmic time to vanish, and weak measurements remain consistent for the total universal wave function without external observers.

What would settle it

Demonstration that applying third quantization to the torsion-extended Hamiltonian causes the cosmic time to vanish, or that weak measurements cannot be defined without collapsing the universal wave function or requiring external observers.

Figures

Figures reproduced from arXiv: 2604.15130 by David Vasak, Johannes Kirsch, Juergen Struckmeier.

Figure 1
Figure 1. Figure 1: Reproduced from Ref. [40] 20This again is analogous to the wave and geometrical optics: Light rays propagate in a direction ν perpendicular to the phase front of the light wave, ν = ∇.S. The eikonal is related to the index of refraction of the medium, S 2 = n 2 . 21The physical importance of deviations from the equilibrium are discussed in [38]. 17 [PITH_FULL_IMAGE:figures/full_fig_p017_1.png] view at source ↗
read the original abstract

We present a theoretical analysis of the WDW approach to quantum cosmology extended to gravity theories with torsion. The dynamics of the FLRW universe is formulated as a classical Hamiltonian problem of point particle mechanics. Unlike in the WDW formalism, the Hamiltonian is not zero, though, and the 3rd quantization does not enforce the cosmic time to vanish. The wave function of the Universe appears as a superposition of eigenfunctions of the quantum Hamiltonian with the cosmic time being the conjugate to its eigenvalues, spatial curvatures. The notion of weak measurement is then introduced to avoid the collapse of the total universal wave function upon measurements of the parameter set describing matter and spacetime. The collapse postulate of the standard Copenhagen quantum theory is discussed and the de Broglie-Bohm interpretation of the effective wave function introduced. The question of the boundary conditions for both, the wave function and the Bohmian guidance equation, is addressed. The corresponding numerical calculations will be published in a separate paper.

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

3 major / 2 minor

Summary. The manuscript presents a conceptual extension of the Wheeler-DeWitt (WDW) quantum cosmology to include torsion. The FLRW dynamics is recast as a non-zero Hamiltonian system, enabling third quantization where the universal wave function is a superposition of eigenfunctions with cosmic time conjugate to spatial curvature eigenvalues. Weak measurements are introduced to measure matter and spacetime parameters without collapsing the wave function, supplemented by a de Broglie-Bohm interpretation and discussion of boundary conditions. All numerical work is deferred to a future publication.

Significance. Should the torsion-induced non-vanishing Hamiltonian and the internal weak-measurement protocol prove consistent, this work could provide a framework for operationalizing measurements in a closed quantum universe, potentially mitigating the problem of time and the measurement problem in quantum gravity. The shift to de Broglie-Bohm for the effective wave function offers an alternative to standard interpretations, but its significance hinges on the rigor of the forthcoming calculations.

major comments (3)
  1. [Hamiltonian formulation (abstract and main text)] The key claim that the Hamiltonian is non-zero (in contrast to standard WDW) is stated without providing the explicit torsion-extended minisuperspace Lagrangian or the resulting Hamiltonian constraint after reduction to point-particle mechanics. This omission makes it impossible to confirm that the non-vanishing property survives the quantization and does not rely on ad hoc choices.
  2. [Weak measurement protocol] The introduction of weak measurements to avoid collapse of the universal wave function lacks an explicit construction of the interaction Hamiltonian or the pointer observable within the closed FLRW+torsion system. Without demonstrating that such a protocol can be defined internally (as required by the closed-system assumption), the claim that parameters can be extracted without collapse remains unsubstantiated and is load-bearing for the central proposal.
  3. [de Broglie-Bohm interpretation] The effective wave function is introduced under the de Broglie-Bohm interpretation, but the specific form of the guidance equation for the trajectories in the extended minisuperspace and the choice of boundary conditions are not derived or specified, leaving the interpretation's implementation unclear.
minor comments (2)
  1. [Abstract] The abstract refers to 'the corresponding numerical calculations' without indicating which observables or parameter sets will be addressed, reducing clarity on the paper's scope.
  2. [Overall manuscript] As a purely conceptual paper with no equations, derivations, or results presented, the manuscript would benefit from at least schematic forms of the key Hamiltonians and measurement operators to aid readability.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment point by point below and will revise the paper to strengthen the presentation of the derivations and constructions.

read point-by-point responses

  1. Referee: The key claim that the Hamiltonian is non-zero (in contrast to standard WDW) is stated without providing the explicit torsion-extended minisuperspace Lagrangian or the resulting Hamiltonian constraint after reduction to point-particle mechanics. This omission makes it impossible to confirm that the non-vanishing property survives the quantization and does not rely on ad hoc choices.

    Authors: We agree that the explicit torsion-extended minisuperspace Lagrangian and the resulting Hamiltonian constraint were omitted from the current manuscript. The work is primarily conceptual, with the non-vanishing Hamiltonian following from the inclusion of torsion in the FLRW dynamics. In the revised version we will add a dedicated section deriving the Lagrangian, performing the reduction to point-particle mechanics, obtaining the Hamiltonian constraint, and verifying that the non-zero value arises directly from the torsion terms and survives quantization without ad hoc choices. revision: yes

  2. Referee: The introduction of weak measurements to avoid collapse of the universal wave function lacks an explicit construction of the interaction Hamiltonian or the pointer observable within the closed FLRW+torsion system. Without demonstrating that such a protocol can be defined internally (as required by the closed-system assumption), the claim that parameters can be extracted without collapse remains unsubstantiated and is load-bearing for the central proposal.

    Authors: The referee correctly identifies that an explicit interaction Hamiltonian and pointer observable for the weak-measurement protocol are not constructed. Because the manuscript focuses on the conceptual framework and defers detailed calculations, these elements were not provided. In revision we will include a schematic but explicit construction of the interaction Hamiltonian and pointer observable, showing how they can be defined internally using the degrees of freedom already present in the closed FLRW+torsion minisuperspace, thereby substantiating that parameters can be extracted without collapse. revision: yes

  3. Referee: The effective wave function is introduced under the de Broglie-Bohm interpretation, but the specific form of the guidance equation for the trajectories in the extended minisuperspace and the choice of boundary conditions are not derived or specified, leaving the interpretation's implementation unclear.

    Authors: We acknowledge that the specific form of the guidance equation in the extended minisuperspace and the detailed choice of boundary conditions were not derived in the manuscript, although the question of boundary conditions was addressed at a conceptual level. In the revised version we will derive the guidance equation from the effective wave function and specify the boundary conditions for both the wave function and the Bohmian trajectories, thereby clarifying the implementation of the interpretation. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation chain is self-contained via torsion extension

full rationale

The paper starts from the standard WDW constraint, augments the gravitational action with torsion, reduces the FLRW dynamics to a point-particle Hamiltonian, and obtains a non-vanishing H that permits third quantization with cosmic time as the conjugate variable to curvature eigenvalues. Weak measurement is introduced as an interpretive device to avoid collapse on the closed system. None of these steps equates a derived quantity to its own input by definition, renames a fitted parameter as a prediction, or relies on a load-bearing self-citation whose content is unverified; the non-zero Hamiltonian follows directly from the torsion term rather than from any prior result of the same authors. Boundary conditions and numerical work are explicitly deferred to a separate paper.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The proposal rests on standard quantum mechanics and FLRW cosmology plus the new torsion extension and the claim that weak measurements can be applied to the closed universe.

axioms (2)
  • domain assumption The dynamics of the FLRW universe can be formulated as a classical Hamiltonian problem of point particle mechanics even when torsion is present.
    Stated directly as the starting point for the analysis.
  • domain assumption Standard quantum mechanics applies to the universe as a whole, including the possibility of a non-vanishing Hamiltonian after 3rd quantization.
    Invoked to allow superposition and time as conjugate variable.
invented entities (1)
  • Effective wave function under de Broglie-Bohm interpretation for the universe no independent evidence
    purpose: To describe definite trajectories and permit weak measurements without collapse of the total wave function
    Introduced to circumvent the Copenhagen collapse postulate for a closed system.

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Works this paper leans on

43 extracted references · 43 canonical work pages

  1. [1]

    John A. Wheeler. On the Nature of quantum geometrodynamics. Annals Phys., 2:604– 614, 1957

    work page 1957

  2. [2]

    Bryce S. DeWitt. Quantum theory of gravity. i. the canonical theory. Phys. Rev., 160:1113–1148, Aug 1967

    work page 1967

  3. [3]

    Setting free the cosmic time in Quantum Universe

    David Vasak. Setting free the cosmic time in Quantum Universe. arXiv preprint gr-qc/2505.01358, 2025

    work page arXiv 2025

  4. [4]

    K. V . Kuchar. Time and interpretations of quantum gravity.Int. J. Mod. Phys. D, 20:3–86, 2011

    work page 2011

  5. [5]

    H. Lorentz. Over Einstein’s theorie der zwaartekracht (iii). Koninklikje Akademie van Wetenschappen the Amsterdam. Verslangen van de Gewone Vergaderingen der Wisen Natuurkundige Afdeeling, 25:468–486, 1916

    work page 1916

  6. [6]

    Levi-Civita

    T. Levi-Civita. On the analytic expression that must be given to the gravitational tensor in Einstein’s theory. Atti della Accademia Nazionale dei Lincei, Rendiconti Lincei, Scienze Fisiche e Naturali., 26(4), 1917. 20

    work page 1917

  7. [7]

    Edward P. Tryon. Is the universe a vacuum fluctuation. Nature, 246:396, 1973

    work page 1973

  8. [8]

    Spontaneous creation of the universe from nothing

    Dongshan He, Dongfeng Gao, and Qing-yu Cai. Spontaneous creation of the universe from nothing. Phys. Rev. D, 89(8):083510, 2014

    work page 2014

  9. [9]

    Covariant Canonical Gauge Grav- ity

    David Vasak, Jürgen Struckmeier, and Johannes Kirsch. Covariant Canonical Gauge Grav- ity. FIAS Interdisc. Sci. Ser., 9783031437175:pp., 2023

    work page 2023

  10. [10]

    Torsion driving cosmic expansion

    Johannes Kirsch, David Vasak, Armin van de Venn, and Jürgen Struckmeier. Torsion driving cosmic expansion. Eur. Phys. J. C, 83(5):425, 2023

    work page 2023

  11. [11]

    Torsional dark energy in quadratic gauge gravity

    Armin van de Venn, David Vasak, Johannes Kirsch, and Jürgen Struckmeier. Torsional dark energy in quadratic gauge gravity. Eur. Phys. J. C, 83(4):288, 2023

    work page 2023

  12. [12]

    Brill and J.A

    D.R. Brill and J.A. Wheeler. Interaction of Neutrinos and Gravitational Fields. Rev. Mod. Phys., 29(3), 1957

    work page 1957

  13. [13]

    D. Atkatz. Quantum cosmology for pedestrians. Am. J. Phys., 62:619–627, 1994

    work page 1994

  14. [14]

    Quantum cosmology.Z

    Claus Kiefer and Barbara Sandhoefer. Quantum cosmology.Z. Naturforsch. A, 77(6):543– 559, 2022

    work page 2022

  15. [15]

    Wheeler-DeWitt Universe Wave Function in the presence of stiff matter

    Francesco Giacosa and Giuseppe Pagliara. Wheeler-DeWitt Universe Wave Function in the presence of stiff matter. Acta Physica Polonica, pages 1607–1622, 2018

    work page 2018

  16. [16]

    J. B. Hartle and S. W. Hawking. Wave Function of the Universe. Phys. Rev. D, 28:2960– 2975, 1983

    work page 1983

  17. [17]

    Perspectives in cosmology

    Alexander Vilenkin. Perspectives in cosmology. Low Temperature Physics, 48(5):378– 382, 05 2022

    work page 2022

  18. [18]

    Infrared Generalized Uncertainty Principles Applied To LRS Bianchi I Quantum Cosmology

    Daniel Berkowitz. Infrared Generalized Uncertainty Principles Applied To LRS Bianchi I Quantum Cosmology. arXiv preprint gr-qc/2011/12442, 2011

    work page 2011

  19. [19]

    Quantum cosmology with vector torsion

    Ammar Kasem and Shaaban Khalil. Quantum cosmology with vector torsion. EPL, 139(1):19002, 2022

    work page 2022

  20. [20]

    Quantum chaos, classical randomness, and bohmian mechanics

    Detlef Dürr, Sheldon Goldstein, and Nino Zanghi. Quantum chaos, classical randomness, and bohmian mechanics. Journal of Statistical Physics, 68:259–270, 1992

    work page 1992

  21. [21]

    Quantum equilibrium and the role of operators as observables in quantum theory

    Detlef Dürr, Sheldon Goldstein, and Nino Zanghì. Quantum equilibrium and the role of operators as observables in quantum theory. Journal of Statistical Physics, 116:959–1055, 2004

    work page 2004

  22. [22]

    Delayed-choice experiments and the bohm approach

    Basil J Hiley and RE Callaghan. Delayed-choice experiments and the bohm approach. Physica Scripta, 74(3):336, 2006

    work page 2006

  23. [23]

    Pilot wave quantum cosmology

    Yuri Shtanov. Pilot wave quantum cosmology. Phys. Rev. D, 54:2564–2570, 1996

    work page 1996

  24. [24]

    Mathematische Grundlagen der Quantenmechanik, volume 38

    John V on Neumann. Mathematische Grundlagen der Quantenmechanik, volume 38. Springer-Verlag, 1932

    work page 1932

  25. [25]

    Relative state

    Hugh Everett III. "Relative state" formulation of quantum mechanics. Reviews of modern physics, 29(3):454, 1957. 21

    work page 1957

  26. [26]

    Many Worlds in Context

    Max Tegmark. Many Worlds in Context. In Simon Saunders, Jonathan Barrett, Adrian Kent, and David Wallace, editors, Many worlds? Everett, quantum theory, and reality, pages 553–581. MIT, 5 2009

    work page 2009

  27. [27]

    De Broglie–Bohm pilot-wave theory: Many worlds in denial

    Antony Valentini. De Broglie–Bohm pilot-wave theory: Many worlds in denial. Many worlds, pages 476–509, 2010

    work page 2010

  28. [28]

    Classical Mechanics: Systems of Particles and Hamiltonian Dynamics

    Walter Greiner. Classical Mechanics: Systems of Particles and Hamiltonian Dynamics. Springer, 2nd edition edition, 2010

    work page 2010

  29. [29]

    A Suggested interpretation of the quantum theory in terms of hidden vari- ables

    David Bohm. A Suggested interpretation of the quantum theory in terms of hidden vari- ables. 2. Phys. Rev., 85:180–193, 1952

    work page 1952

  30. [30]

    A Suggested interpretation of the quantum theory in terms of hidden vari- ables

    David Bohm. A Suggested interpretation of the quantum theory in terms of hidden vari- ables. 1. Phys. Rev., 85:166–179, 1952

    work page 1952

  31. [31]

    Quantum theory without observers—part two

    Sheldon Goldstein. Quantum theory without observers—part two. Physics Today, 51(4):38–42, 04 1998

    work page 1998

  32. [32]

    Bohmian mechan- ics and quantum field theory

    Detlef Dürr, Sheldon Goldstein, Roderich Tumulka, and Nino Zanghi. Bohmian mechan- ics and quantum field theory. Phys. Rev. Lett., 93:090402, 2004

    work page 2004

  33. [33]

    Why isn’t every physicist a bohmian? arXiv preprint quant-ph/0412119, 2004

    Oliver Passon. Why isn’t every physicist a bohmian? arXiv preprint quant-ph/0412119, 2004

    work page arXiv 2004

  34. [34]

    An Introduction to the Study of WaveMechanics

    Louis de Broglie. An Introduction to the Study of WaveMechanics. Methuen & Co. Ltd., London, 1930

    work page 1930

  35. [35]

    On waves and particles

    Nathan Rosen. On waves and particles. Journal of the Elisha Mitchell Scientific Society, 61(1/2):67–73, 1945

    work page 1945

  36. [36]

    Non-commutative quantum geometry: a reappraisal of the bohm approach to quantum theory

    J Hiley. Non-commutative quantum geometry: a reappraisal of the bohm approach to quantum theory. In Quo Vadis Quantum Mechanics?, pages 299–324. Springer, 2005

    work page 2005

  37. [37]

    Speakable and unspeakable in quantum mechanics: Collected papers on quantum philosophy

    John Stewart Bell. Speakable and unspeakable in quantum mechanics: Collected papers on quantum philosophy. Cambridge university press, 2004

    work page 2004

  38. [38]

    Pilot-wave theory and the search for new physics

    Antony Valentini. Pilot-wave theory and the search for new physics. arXiv preprint gr-qc/2411.10782, 2024

    work page arXiv 2024

  39. [39]

    Quantum interference and the quan- tum potential

    Chris Philippidis, Chris Dewdney, and Basil J Hiley. Quantum interference and the quan- tum potential. Nuovo Cimento B, 52(1):15–28, 1979

    work page 1979

  40. [40]

    Bohm’s approach to quantum mechanics: Alternative theory or practical picture? Frontiers of Physics, 14:1–15, 2019

    AS Sanz. Bohm’s approach to quantum mechanics: Alternative theory or practical picture? Frontiers of Physics, 14:1–15, 2019

    work page 2019

  41. [41]

    Quantum mechanics in a time-asymmetric universe: On the nature of the initial quantum state

    Eddy Keming Chen. Quantum mechanics in a time-asymmetric universe: On the nature of the initial quantum state. The British Journal for the Philosophy of Science, 2021

    work page 2021

  42. [42]

    J. S. Bell. On the Einstein-Podolsky-Rosen paradox. Physics Physique Fizika, 1:195–200, 1964

    work page 1964

  43. [43]

    The Bohm interpretation of quantum cosmology

    Nelson Pinto-Neto. The Bohm interpretation of quantum cosmology. Found. Phys., 35:577–603, 2005

    work page 2005