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REVIEW 3 major objections 1 minor 56 references

An approximate application of quantum gravity to the rotation problem

T0 review · 3 major / 1 minor · reviewed 2026-06-27 · grok-4.3

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Pith's one-line read Quantum gravity path integrals suppress relative cosmic rotation to extremely small values through phase interference.

desk verdict The paper sketches a path-integral argument that quantum gravity suppresses cosmic rotation via phase cancellation, but the bound is set by restricting the integral to a one-parameter family and by external inputs like e-foldings. read the letter →

arxiv 2606.12461 v1 pith:WM35MRHF submitted 2026-06-08 gr-qc

R. Michael Jones This is my paper · ORCID
classification gr-qc
keywords quantumgravitypathintegralrotationproblemEinstein-Hilbertactioncosmicphaseinterferenceinflationcosmology
topics Quantum Gravity
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 establishes that nearly any quantum gravity theory, when using a path integral over different possible cosmologies, will have destructive interference that eliminates contributions from those with large relative rotation between matter and inertial frames. This happens because the Einstein-Hilbert action reaches an extremum at zero rotation rate, leading to phase cancellation for nonzero rates. The effect is strong enough to limit significant contributions to rotation rates below 10^{-51} rad/year after 50 e-foldings of inflation. A reader should care because this mechanism explains the observed near-zero rotation without relying on special initial conditions or fine-tuning in general relativity.

What carries the argument

The path integral over a family of classical cosmologies differing in rms relative rotation rate, with each path weighted by its Einstein-Hilbert action value.

What would settle it

A measurement or observation showing a relative rotation rate between matter and inertial frames exceeding 10^{-51} rad/year in the present universe would contradict the prediction.

Watch

Extended reading notes

Core claim

The path integral calculation over classical cosmologies that differ only in their rms relative rotation rate, weighted by the Einstein-Hilbert action, shows that the action is an extremum at zero rms relative rotation rate. Phase interference then limits the cosmologies that contribute significantly to those with relative rms rotation rates less than about 10^{-51} rad/year after 50 e-foldings during inflation. The result is insensitive to the specific details of the quantum gravity theory.

Load-bearing premise

The path integral is performed only over classical cosmologies that differ solely in their rms relative rotation rate, each weighted by the Einstein-Hilbert action evaluated on that cosmology.

Editorial extensions

If this is right

  • The limit on rotation holds even without inflation, at about 10^{-32} rad/year a quarter second after the singularity.
  • Greater numbers of e-foldings during inflation produce even stricter upper bounds on the allowed rotation rate.
  • The suppression occurs as early as a quarter of a second after the initial singularity.
  • The bound depends primarily on the visible universe size, Planck time, speed of light, Hubble parameter, and number of e-foldings.

Reading between the lines

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

  • If the mechanism works, it could apply similarly to other cosmological fine-tuning problems like the flatness or horizon problem by the same phase interference.
  • Precise measurements of any residual cosmic rotation could test the exact number of e-foldings assumed.
  • Extending the calculation to include quantum corrections beyond the Einstein-Hilbert action might refine the bound but is unlikely to change the order of magnitude.
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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

3 major / 1 minor

Summary. The manuscript claims that an approximate path-integral treatment of quantum gravity using the Einstein-Hilbert action, restricted to a one-parameter family of classical cosmologies differing only by their rms relative rotation rate, yields an extremum of the action at zero rotation. Phase interference then suppresses contributions from non-zero rates, limiting significant contributors to rms rates below ~10^{-51} rad/yr after 50 e-foldings (or ~10^{-32} rad/yr without inflation), thereby solving the rotation problem; the bound is stated to depend only on the visible-universe size, Planck time, c, H, and the externally chosen e-folding number.

Significance. If the modeling assumptions were justified, the result would supply a quantum-gravity mechanism that automatically selects near-zero rotation without fine-tuned initial conditions and would be largely insensitive to the ultraviolet completion. The approach explicitly credits the use of the Einstein-Hilbert action evaluated on classical solutions and the resulting phase factor exp(i S_EH / ħ). However, the numerical bound is obtained by direct substitution of observed cosmological parameters and an assumed e-folding count, so the smallness is an input rather than an output of the dynamics.

major comments (3)
  1. [Abstract] Abstract and the paragraph beginning 'These calculations are based on using 50 e-foldings': the reported upper limit is obtained by inserting the observed Hubble parameter, the size of the visible universe, and an assumed 50 e-foldings into the action difference; the smallness of the final number is therefore fixed by these prior cosmological inputs rather than derived from any dynamical suppression inside the theory.
  2. [Abstract] Abstract, sentence 'The calculation shows that the action is an extremum at zero rms relative rotation rate': the path integral is performed over a family of classical cosmologies that differ only in their rms relative rotation rate, each weighted by the Einstein-Hilbert action evaluated on that cosmology; the reduction of the measure to an integral over this single parameter while freezing all other metric degrees of freedom is an external modeling choice not derived from a controlled limit of the full diffeomorphism-invariant path integral.
  3. [Abstract] Abstract, final paragraph: non-classical or non-FLRW configurations are simply omitted, yet the central claim requires that the phase factor produces destructive interference for any rms rotation rate ≳ 10^{-51} rad/yr; this holds only inside the chosen one-parameter slice.
minor comments (1)
  1. [Abstract] The abstract states the result but provides no explicit derivation of the phase-interference integral or error estimates; adding a short section with the explicit integral and its evaluation would improve clarity.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful review and constructive comments on our approximate calculation. We respond point-by-point to the major comments below.

read point-by-point responses

  1. Referee: [Abstract] Abstract and the paragraph beginning 'These calculations are based on using 50 e-foldings': the reported upper limit is obtained by inserting the observed Hubble parameter, the size of the visible universe, and an assumed 50 e-foldings into the action difference; the smallness of the final number is therefore fixed by these prior cosmological inputs rather than derived from any dynamical suppression inside the theory.

    Authors: We agree that the specific numerical upper limit is computed by substituting standard observed values (Hubble parameter, visible-universe size) and an assumed e-folding number into the action difference. These quantities are not tuned for the rotation problem but are taken from independent cosmological data and models. The dynamical content of the calculation is the phase-interference suppression that follows once the action difference is evaluated; the result shows that the observed smallness does not require additional fine-tuning beyond these known inputs. We will revise the abstract to make this distinction explicit. revision: partial

  2. Referee: [Abstract] Abstract, sentence 'The calculation shows that the action is an extremum at zero rms relative rotation rate': the path integral is performed over a family of classical cosmologies that differ only in their rms relative rotation rate, each weighted by the Einstein-Hilbert action evaluated on that cosmology; the reduction of the measure to an integral over this single parameter while freezing all other metric degrees of freedom is an external modeling choice not derived from a controlled limit of the full diffeomorphism-invariant path integral.

    Authors: The paper's title states that this is 'An approximate application,' precisely to indicate that the reduction to a one-parameter family of classical solutions is a deliberate modeling choice that isolates the rotation degree of freedom. A controlled derivation of the measure from the full diffeomorphism-invariant path integral would require a complete ultraviolet-complete quantum gravity theory, which lies outside the scope of the present work. The approximation is sufficient to exhibit the extremum of the Einstein-Hilbert action at zero rotation and the resulting interference effect. revision: no

  3. Referee: [Abstract] Abstract, final paragraph: non-classical or non-FLRW configurations are simply omitted, yet the central claim requires that the phase factor produces destructive interference for any rms rotation rate ≳ 10^{-51} rad/yr; this holds only inside the chosen one-parameter slice.

    Authors: We acknowledge that the demonstrated destructive interference applies within the restricted one-parameter family of classical FLRW-like cosmologies. The central claim of the manuscript is that this simplified setting already illustrates a quantum-gravity mechanism capable of suppressing relative rotation via phase cancellation. Extending the calculation to non-classical or non-FLRW metrics would require a more complete framework that is not yet available; the present result is offered as an approximate illustration rather than a exhaustive proof. revision: no

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; bound derived from explicit action evaluation on parameterized family

full rationale

The paper evaluates the Einstein-Hilbert action on a one-parameter family of classical cosmologies differing by rms relative rotation rate, shows the action extremum at zero rotation (by direct computation on those solutions), and then uses the resulting phase factor exp(i S / ħ) to obtain an interference bound. The numerical upper limit on rotation rate is obtained by substituting external inputs (visible-universe size, Hubble parameter, Planck time, and an assumed 50 e-foldings) into the action difference; this is a forward calculation, not a redefinition or statistical fit of the output to itself. No self-citation chain, uniqueness theorem, or ansatz smuggling is invoked to close the argument. The modeling restriction to classical FLRW slices is stated as an approximation, not hidden inside the equations as a tautology. The derivation therefore remains self-contained against its stated inputs.

Assumptions & free parameters 2 free parameters · 2 assumptions · 0 invented entities

The central numerical bounds rest on the Einstein-Hilbert action evaluated on rotating cosmologies, the assumption that the path integral is dominated by classical histories differing only in rotation rate, and the external choice of 50 e-foldings during inflation.

free parameters (2)
  • number of e-foldings = 50
    Taken as 50 (or 55-60) to obtain the 10^{-51} bound; directly controls the size of the action difference that produces the phase cancellation.
  • Hubble parameter at early times
    Enters the action difference that sets the rotation-rate cutoff.
assumptions (2)
  • domain assumption The path integral in quantum gravity can be approximated by a sum over classical cosmologies that differ only in their rms relative rotation rate, each weighted by the Einstein-Hilbert action.
    Stated in the abstract as the basis for the phase-interference calculation.
  • domain assumption The Einstein-Hilbert action remains the correct effective action for large-scale relative rotation even in the quantum-gravity regime.
    The abstract specifies that the calculation uses the Einstein-Hilbert action including large-scale relative rotation.

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Cite this review

Pith. "Pith review of An approximate application of quantum gravity to the rotation problem." pith.science (2026). https://pith.science/paper/WM35MRHF

@misc{pith2026260612461,
  author       = {Pith},
  title        = {Pith review of: An approximate application of quantum gravity to the rotation problem},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WM35MRHF}},
  note         = {Machine review of arXiv:2606.12461}
}
abstract

Arbitrary initial conditions allow solutions of Einstein's field equations for General Relativity to have arbitrarily large relative rotation of matter and inertial frames. The ``Rotation Problem'' is to explain why the measured relative rotation rate is so small. Nearly any reasonable theory of quantum gravity can solve the rotation problem by phase interference. Even as early as about a quarter of a second after the initial singularity, quantum cosmology would limit the cosmologies that contribute significantly to a path integral calculation to have relative rms rotation rates less than about $10^{-51}$ rad/year. Those calculations are based on using 50 e-foldings during inflation. For 55 or 60 e-foldings, the cosmologies contributing significantly to the path integral would have even smaller relative rotation rates. In addition, although inflation dominates the calculation, even if there had been no inflation, the cosmologies contributing significantly to the path integral would have relative rotation rates less than about $10^{-32}$ rad/year at about a quarter of a second after the initial singularity. These calculations are insensitive to the details of the theory of quantum gravity because the main factor depends only on the size of the visible universe, the Planck time, the free-space speed of light, the Hubble parameter, and the number of e-foldings during inflation. These calculations use the Einstein-Hilbert action in quantum gravity, including large-scale relative rotation of inertial frames and the matter distribution, in which each ``path'' is a cosmology with a different rms relative rotation rate. The calculation shows that the action is an extremum at zero rms relative rotation rate.

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