Pith. sign in

REVIEW 4 major objections 5 minor 55 references

This paper claims that MOND and its deep-MOND law v⁴=2GMa_bg emerge as a quantum second-moment spectral broadening effect, with a_bg = √(Λ/48), rather than as a modification of gravity or force laws.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-02 23:10 UTC pith:OCECT67U

load-bearing objection Genuinely new mechanism for MOND from second-order spectral broadening, but the bridge from broadening to dynamics is asserted via an unproven quantum equivalence principle, and the predicted a0 is off by a factor of 2.2. the 4 major comments →

arxiv 2602.14515 v2 pith:OCECT67U submitted 2026-02-16 gr-qc astro-ph.HEhep-th

MOND from Second-Order Moment Modified Acceleration and Quantum Equivalence Principle

M.J.Luo This is my paper
classification gr-qc astro-ph.HEhep-th
keywords MONDModified Newtonian Dynamicsde Sitter backgroundspectral line broadeningsecond-order momentquantum equivalence principleTully-Fisher relationcosmological constant
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper tries to establish that the anomalous galaxy-rotation behavior known as MOND is neither a modification of gravity nor of Newton's law of force, but a quantum effect on the second moment (variance) of a test particle's spectrum. Local short-time acceleration and the de Sitter background both add universal spectral broadening; when combined, they give an effective acceleration a_eff = sqrt((a_N + a_bg)^2 − a_bg^2) with a_bg = sqrt(Λ/48). In the deep-MOND limit this reproduces the baryonic Tully-Fisher law v⁴ = 2 G M a_bg and predicts the MOND constant a0 ≈ 2.6×10⁻¹⁰ m/s², close to the observed value. The author argues this unifies dark energy and galactic rotation anomalies under one mechanism and requires a quantum equivalence principle that elevates second-moment quantum fluctuations to real accelerations.

Core claim

The paper's central claim is that the deep-MOND scaling v⁴ ≈ 2 G M a_bg follows from the second-order moment (variance) correction to a free particle's action, not from any first-order modification of the geodesic or force law. A locally short-time accelerated frame is connected to an inertial frame by a coordinate shift whose quantization produces an extra spectral broadening (δω)² = (2a)², and a de Sitter background produces an analogous broadening with a_bg = sqrt(Λ/48). Composing the two yields the interpolation a_eff² = (a_N + a_bg)² − a_bg², which interpolates smoothly between Newtonian dynamics and MOND. The author takes this to mean that MOND is a genuine quantum effect—the MOND cons

What carries the argument

The central object is the second-order moment (variance) of a test particle's frequency spectrum. Under local short-time acceleration the variance acquires an extra term (2a)²; in a de Sitter background the variance acquires a similar term with background acceleration a_bg = sqrt(Λ/48). These are encapsulated in modification factors Z_acc and Z_dS multiplying the flat metric in the free-particle action, giving the combination Z_eff = 1 + (4a² − Λ/12) δs². As a result the effective squared acceleration is a_eff² = a_T² − Λ/48, and for circular galaxy orbits this yields the acceleration interpolation a_eff = sqrt((a_N + a_bg)² − a_bg²). This mechanism carries the entire argument: the universal

Load-bearing premise

The load-bearing premise is the quantum equivalence principle: that the universal second-moment broadening of a particle's spectrum is physically equivalent to a real acceleration and therefore must modify the equations of motion; without this step, the computed broadening remains a measurement artifact with no effect on galactic kinematics.

What would settle it

A high-precision measurement of a spectral line's variance under a known short-time acceleration in a well-isolated system, which finds no extra (2a)² broadening, would falsify the core effect. Alternatively, a galaxy whose radial acceleration relation in the transition region differs measurably from the specific function sqrt((a_N + a_bg)² − a_bg²) would falsify the proposed composition rule.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • MOND's interpolation function is no longer free but fixed to the specific form of Eq. (21) for isolated systems.
  • The MOND constant a0 is determined by the cosmological constant: a0 ≈ 2 sqrt(Λ/48) ≈ 2.6×10⁻¹⁰ m/s², the same order as the measured value.
  • The deep-MOND Tully-Fisher relation v⁴ = 2 G M a_bg follows without dark matter, and an analogous Faber-Jackson-type scaling for elliptical galaxies arises from isotropized velocity dispersion.
  • Dark energy (accelerated cosmic expansion) and galactic rotation anomalies become two manifestations of a single second-moment spectral broadening mechanism.
  • Because the effect is kinematic rather than a change of the metric, it sidesteps the no-go obstruction that blocks covariant metric-based modified-gravity formulations of MOND.

Where Pith is reading between the lines

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

  • The predicted value 2a_bg ≈ 2.6×10⁻¹⁰ m/s² is about twice the empirically fitted a0 ≈ 1.2×10⁻¹⁰ m/s²; if the mechanism is right, the discrepancy suggests a missing factor, e.g., in the moment-to-acceleration correspondence or a modified coefficient, that future data could pin down.
  • The second-moment composition rule implies that the interpolation should be tested not only in rotation curves but in any system where acceleration is measured through spectral variance, such as gravitational lensing or high-redshift supernova profiles; deviations would discriminate this mechanism from other MOND derivations.
  • Because the broadening is universal and mass-independent, the framework suggests a search for tiny variance broadening of spectral lines in laboratory atomic clocks or ion traps under controlled short-time accelerations, though the predicted scale is small.

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

4 major / 5 minor

Summary. The paper proposes that a local short-time acceleration of a test particle produces an extra second-order-moment (variance) broadening of its spectrum, with magnitude (2a)^2, and that the de Sitter background produces an analogous effect that can be represented by a background acceleration a_bg = sqrt(Λ/48). Combining the two effects leads to the effective acceleration relation a_eff^2 = (a_N + a_bg)^2 − a_bg^2 (Eq. 21), which reproduces the deep-MOND Tully-Fisher relation v_f^4 ≈ 2GM a_bg (Eq. 23). The paper claims this predicts a0 ≈ 2a_bg ≈ 2.6×10^-10 m/s^2, and it invokes a 'quantum equivalence principle' from the author's prior work as the physical bridge that turns spectral broadening into modified kinematics.

Significance. If the derivation were valid, the paper would supply a concrete, falsifiable origin for MOND's critical acceleration from the cosmological constant and a specific interpolation function. It also generalizes the Unruh/de Sitter temperature idea to short-time non-uniform acceleration and is unusually candid about its limitations, such as the undefined direction of a_eff and the rough treatment of elliptical galaxies. However, the central claim rests on an assumed quantum equivalence principle that is cited to prior self-referenced work rather than derived here, and the numerical prediction for a0 is about a factor 2.2 above the fitted value. In its present form, the paper is a suggestive reinterpretation rather than a derivation.

major comments (4)
  1. [§IV, Eqs. (16)–(21)] Equation (21) is not derived from the action. In Eq. (16) the effective factor Z_eff multiplies the flat metric as a scalar; varying S = m∫ds sqrt(Z_eff η_μν xdot^μ xdot^ν) at fixed Z_eff gives a standard geodesic equation in a conformally flat metric and does not produce a_eff^2 = a_T^2 − a_bg^2 as an equation of motion. The paper bridges this gap by asserting that second-order moment broadening modifies any squared-order mechanical quantity and by invoking the quantum equivalence principle [42]. Since [42] is the author's prior work and is not derived in this manuscript, the MOND interpolation relation is effectively inserted by assumption. Without this step, the spectral broadening computed in §II remains a measurement artifact with no demonstrated effect on v(r).
  2. [§II, Eqs. (2)–(9)] The derivation of Z_acc is not rigorous. The coordinate transformation x^μ → x^μ + a^μ δs^2 leaves dx^μ/ds unchanged if δs is constant, so the action is unchanged; if δs is instead a variable short-time window, its s-dependence must be included and the Fourier replacement δs ∼ ω^{-1} is an ad hoc assumption, not derived. The claimed universal broadening ⟨δω^2⟩ = (2a)^2 depends critically on that replacement. This is the physical input that later produces a_bg and Eq. (21), so the foundation of the prediction is not yet established.
  3. [§IV, Eq. (23); §V(7)] The quantitative prediction is a0 = 2a_bg ≈ 2.6×10^-10 m/s^2, while the fitted MOND constant is a0 ≈ 1.2×10^-10 m/s^2. The ratio is 2.2. Describing this as 'very close' is not acceptable for a claimed derivation of a fundamental constant. The deep-MOND normalization v^4 = GM a0 fixes the coefficient, so the discrepancy cannot be absorbed by a different interpolation function. The paper needs to identify a source of a factor ~2 or revise the claimed prediction.
  4. [§IV, Eq. (19)] The acceleration composition rule a_T = a_pr + a_bg is asserted rather than derived. The paper acknowledges that a_eff^2 determines only the squared magnitude and that the direction of a_eff is not fixed, but then 'simply attribute[s]' a_eff^2 to a single radial component in spiral galaxies. This is a strong assumption for a rotation-curve application and needs justification beyond the statement that the radial component is dominant. The manuscript does not provide a calculation showing how the isotropic background acceleration combines with a proper acceleration in the equations of motion.
minor comments (5)
  1. [General] The text contains numerous typographical and spacing errors (e.g., 'thepaper', 'deSitter' instead of 'de Sitter', missing spaces around equations). A careful editing pass is needed.
  2. [§V(7)] The displayed expression for a0 is typographically ambiguous. If intended as a0 = 2a_bg = (1/(2√3))√Λ, it is algebraically consistent with a_bg = √(Λ/48). Please disambiguate the fraction so that the correct reading is unambiguous.
  3. [§III] The numerical value a_bg ≈ 1.3×10^-10 m/s^2 is quoted from q0 ≈ −0.64 and H0, but the explicit formula and the dependence on q0 and H0 are not given. This makes it difficult to assess the uncertainty in the predicted a0.
  4. [§IV, Eq. (15)] The distance-redshift relation in Eq. (15) claims an extra broadening term in ⟨z^2⟩, but the standard FRW luminosity distance already contains the (1 − q0)⟨z⟩^2 term. The paper should clarify how the new contribution is separated from the standard cosmological acceleration effect.
  5. [References] The quantum equivalence principle is central to the argument and is supported mainly by the author's own prior papers [42,47]. Please provide a self-contained statement, and preferably a derivation, of this principle in this manuscript.

Circularity Check

2 steps flagged

Eq. (21) is a definitional consequence of Z_eff via the self-cited 'quantum equivalence principle,' not an independent prediction.

specific steps
  1. self definitional [Sec. IV, Eqs. (16)-(21)]
    "Zef f= 1 + (4a^2 − Λ/12) δs^2 ≡ 1 + 4a^2_eff δs^2 ... and a^2_eff = a^2_T − Λ/48 ... As a consequence, we obtain the acceleration interpolation function v(r)^2/r = a^r_eff = sqrt((a_N + a_bg)^2 − a^2_bg)"

    Eq. (17) defines a_eff through the explicit symbol '≡', and Eq. (18) fixes a_eff^2 = a_T^2 − Λ/48. Inserting a_T = a_pr + a_bg and a_bg^2 = Λ/48 (Eq. 14) makes Eq. (21) hold identically. The action (16) itself is just the flat action multiplied by the scalar factor Z_eff; varying it does not produce a new equation of motion containing a_eff. Thus the central 'interpolation relation' is a definitional relabeling of Z_eff, not a consequence independently derived from the action.

  2. self citation load bearing [Sec. IV, paragraph preceding Eq. (21); Refs. [42], [47]]
    "Therefore, the proposed Modified Inertial interpretation requires a quantum equivalence principle [42] as its physical foundation. Specifically, the universal part of the second-order moment fluctuation in the test particle’s spectrum (or coordinates) is indistinguishable from the acceleration of its comoving coordinate system..."

    This is the load-bearing bridge from the spectral broadening computed in Secs. II-III to the modified orbital kinematics used in Eq. (21). The principle is not derived in this paper but is attributed to the author's own prior work (Ref. [42], and relatedly [47]). Without granting the quantum equivalence principle, the second-moment broadening is only a feature of the spectrum and has no demonstrated effect on v^2/r. Therefore the paper's main MOND result is logically equivalent to accepting a self-cited, unverified postulate that already contains the needed acceleration-equivalence.

full rationale

The paper does contain a self-contained calculation of second-moment spectral broadening from short-time acceleration and from a de Sitter background. That part is independent and could stand as a physical effect on its own. However, the MOND relation is not obtained from that calculation alone. The decisive step is Eq. (17), where a_eff is introduced by '≡', and Eq. (18), where its square is fixed; Eq. (21) then follows algebraically once a_T is set to a_N + a_bg. The only physical input making that definition relevant to galactic rotation is the quantum equivalence principle, which is asserted and cited to the author's prior paper [42] without independent derivation or verification here. Thus the central prediction reduces by construction to a self-cited principle. I do not score this higher because the spectral-broadening computation is non-trivial and the paper makes a concrete, falsifiable numerical comparison; moreover, the predicted a0 = 2a_bg ≈ 2.6e-10 m/s^2 is actually a factor of about 2.2 larger than the fitted a0 ≈ 1.2e-10 m/s^2, so it is not a simple recitation of the fitted MOND constant. Still, the derivation chain of the MOND interpolation is circular in the sense that Eq. (21) is built into the definition of a_eff and the quantum equivalence principle that activates it is self-cited and unproven.

Axiom & Free-Parameter Ledger

1 free parameters · 6 axioms · 1 invented entities

The derivation rests on a set of assumptions drawn from the author's prior framework, most importantly the quantum equivalence principle. No free parameter is fitted to the Tully-Fisher data; the predicted a0 is derived, but the derivation depends on the ad hoc δs~1/ω identification and on vectorially adding accelerations without derivation.

free parameters (1)
  • characteristic spectral time δs = δs ~ 1/ω
    The short-time acceleration interval is identified with the inverse Fourier frequency (Sec. II), an ad hoc identification that converts the coordinate transformation parameter into the observed spectral broadening.
axioms (6)
  • ad hoc to paper Quantum equivalence principle: universal second-order moment spectral broadening is indistinguishable from real acceleration and modifies kinematics
    Assumed from the author's prior work [42]; it is the bridge from spectral effects to equations of motion (Secs. IV-V).
  • ad hoc to paper δs ~ ω^{-1}
    Identifies the short-time interval with the spectral period (Sec. II), needed to turn Z_acc into ω² + 4a².
  • domain assumption Vector composition a_T = a_pr + a_bg
    Stated in Sec. IV Eq. (19) on physical grounds (uniform isotropic background), no derivation.
  • domain assumption Linear superposition of acceleration and deSitter corrections Z_eff = 1 + (4a² - Λ/12)δs²
    Assumes the two small corrections simply add (Eq. 17).
  • standard math Metric expansion of deSitter background to second order with coefficient 1/3
    Eq. (10), standard Riemann normal coordinate expansion; not the problematic step.
  • domain assumption Effective acceleration a_eff² can be attributed to a single radial component in spiral galaxies
    Justified only for the special case; acknowledged as a limitation in Sec. V(4).
invented entities (1)
  • Universal second-order moment quantum fluctuation of spacetime no independent evidence
    purpose: To reinterpret the extra spectral broadening as a property of spacetime rather than of the particle, enabling the quantum equivalence principle.
    Introduced in Sec. II and prior work [42,47]; no falsifiable handle is given beyond the claimed broadening effect itself, which the paper says is too small to detect in the lab.

pith-pipeline@v1.3.0-alltime-deepseek · 12520 in / 22223 out tokens · 206213 ms · 2026-08-02T23:10:59.681176+00:00 · methodology

0 comments
read the original abstract

This paper proposes a novel non-inertial quantum effect wherein particle spectra show second-order moment extra Gaussian broadening due to local short-time (non-uniform) acceleration, as well as in a deSitter spacetime background. Although the effect is too small to be detected, it provides a mechanism for the cosmological constant to enter the local kinematics of particles in the form of acceleration. The acceleration composition relation of a proper motion acceleration and the cosmological constant playing the role of a background acceleration, which is required in the Modified Newtonian Dynamics (MOND). In this framework, MOND arises from the second-order moment correction to the squared-acceleration due to the non-inertial quantum effect of the deSitter background, rather than first-order moment correction to the classical geodesic equation of motion, which differs from most of the literature attempting to derive MOND, which can be confirmed or falsified in future high-precision measurements. The interpretation of MOND as a second moment effect necessitates a quantum equivalence principle as its physical foundation, that is, extending the classical equivalence at the level of mean values (first-order moments) to the quantum equivalence at the level of second moment quantum fluctuations. The effective distance quadratic form, effective curvature and effective acceleration, etc., modified by the universal second moments all behave as if they were real geometrical or physical quantities. This effect also offers a unified framework for understanding the accelerated expansion of the universe and the anomalies in galactic rotation curves or radial acceleration.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

55 extracted references · 3 linked inside Pith

  1. [1]

    free fall

    This extra broadening is indistinguishable from the universal extra broadening (9) caused by general acceleration. In fact, observational results from the late-epoch universe dominated by a positive cosmological constant (ordarkenergy)andexperiencingacceleratedexpansioncouldentirelystemfromthecorrectiontothedistance-redshift relation at the second-order i...

  2. [2]

    M. A. Milgrom. A modification of the newtonian dynamics as a possible alternative to the hidden mass hypothesis.The Astrophysical Journal, 270(2):365–370, 1983

    1983

  3. [3]

    MOND theory.Can

    Mordehai Milgrom. MOND theory.Can. J. Phys., 93(2):107–118, 2015

    2015

  4. [4]

    Scale Invariance at low accelerations (aka MOND) and the dynamical anomalies in the Universe

    Mordehai Milgrom. Scale Invariance at low accelerations (aka MOND) and the dynamical anomalies in the Universe. Fortsch. Phys., 65(6-8):1600046, 2017

    2017

  5. [5]

    Modified Newtonian Dynamics (MOND): Observational Phenomenology and Rela- tivistic Extensions.Living Rev

    Benoit Famaey and Stacy McGaugh. Modified Newtonian Dynamics (MOND): Observational Phenomenology and Rela- tivistic Extensions.Living Rev. Rel., 15:10, 2012

    2012

  6. [6]

    The MOND paradigm of modified dynamics.Scholarpedia, 9(6):31410, 2014

    Mordehai Milgrom. The MOND paradigm of modified dynamics.Scholarpedia, 9(6):31410, 2014

    2014

  7. [7]

    Mordehai Milgrom. MOND vs. dark matter in light of historical parallels.Stud. Hist. Phil. Sci. B, 71:170–195, 2020

    2020

  8. [8]

    Modified Newtonian Dynamics (MOND).arXiv:2501.17006, 1 2025

    Benoit Famaey and Amel Durakovic. Modified Newtonian Dynamics (MOND).arXiv:2501.17006, 1 2025

    Pith/arXiv arXiv 2025

  9. [9]

    Radial Acceleration Relation in Rotationally Supported Galaxies

    Stacy McGaugh, Federico Lelli, and Jim Schombert. Radial Acceleration Relation in Rotationally Supported Galaxies. Phys. Rev. Lett., 117(20):201101, 2016

    2016

  10. [10]

    Bimetric MOND gravity.Phys

    Mordehai Milgrom. Bimetric MOND gravity.Phys. Rev. D, 80:123536, 2009

    2009

  11. [11]

    MOND and its bimetric formulation

    Mordehai Milgrom. MOND and its bimetric formulation. InRencontres du Vietnam: Hot Topics in General Relativity and Gravitation, 10 2013

    2013

  12. [12]

    Broader view of bimetric MOND.Phys

    Mordehai Milgrom. Broader view of bimetric MOND.Phys. Rev. D, 106(8):084010, 2022

    2022

  13. [13]

    Bekenstein and Mordehai Milgrom

    J. Bekenstein and Mordehai Milgrom. Does the missing mass problem signal the breakdown of Newtonian gravity? Astrophys. J., 286:7–14, 1984

    1984

  14. [14]

    Quasi-linear formulation of MOND.Mon

    Mordehai Milgrom. Quasi-linear formulation of MOND.Mon. Not. Roy. Astron. Soc., 403:886, 2010

    2010

  15. [15]

    Bekenstein

    Jacob D. Bekenstein. Relativistic gravitation theory for the MOND paradigm.Phys. Rev. D, 70:083509, 2004. [Erratum: Phys.Rev.D 71, 069901 (2005)]

    2004

  16. [16]

    The Tensor-Vector-Scalar theory and its cosmology.Class

    Constantinos Skordis. The Tensor-Vector-Scalar theory and its cosmology.Class. Quant. Grav., 26:143001, 2009

    2009

  17. [17]

    T. G. Zlosnik, P. G. Ferreira, and Glenn D. Starkman. The Vector-tensor nature of Bekenstein’s relativistic theory of modified gravity.Phys. Rev. D, 74:044037, 2006

    2006

  18. [18]

    Dynamics with a non-standard inertia-acceleration relation: an alternative to dark matter.Annals Phys., 229:384–415, 1994

    Mordehai Milgrom. Dynamics with a non-standard inertia-acceleration relation: an alternative to dark matter.Annals Phys., 229:384–415, 1994

    1994

  19. [19]

    MOND–particularly as modified inertia.Acta Phys

    Mordehai Milgrom. MOND–particularly as modified inertia.Acta Phys. Polon. B, 42:2175–2184, 2011

    2011

  20. [20]

    Models of a modified-inertia formulation of MOND.Phys

    Mordehai Milgrom. Models of a modified-inertia formulation of MOND.Phys. Rev. D, 106(6):064060, 2022

    2022

  21. [21]

    MOND as manifestation of modified inertia

    Mordehai Milgrom. MOND as manifestation of modified inertia. 10 2023

    2023

  22. [22]

    Towards an interpretation of MOND as a modification of inertia.Mon

    Fathi Namouni. Towards an interpretation of MOND as a modification of inertia.Mon. Not. Roy. Astron. Soc., 452(1):210– 216, 2015

    2015

  23. [23]

    Modified Newtonian Dynamics (MOND) as a Modification of Newtonian Inertia.Journal of Astro- physics and Astronomy, 38(4):59, December 2017

    Mohammed Alzain. Modified Newtonian Dynamics (MOND) as a Modification of Newtonian Inertia.Journal of Astro- physics and Astronomy, 38(4):59, December 2017

    2017

  24. [24]

    Renato Costa, Guilherme Franzmann, and Jonas P. Pereira. A local Lagrangian for MOND as modified inertia. arXiv:1904.07321, 4 2019

    Pith/arXiv arXiv 1904

  25. [25]

    Noncovariance at low accelerations as a route to MOND.Phys

    Mordehai Milgrom. Noncovariance at low accelerations as a route to MOND.Phys. Rev. D, 100(8):084039, 2019

    2019

  26. [26]

    Bernal, S

    T. Bernal, S. Capozziello, J. C. Hidalgo, and S. Mendoza. Recovering MOND from extended metric theories of gravity. Eur. Phys. J. C, 71:1794, 2011

    2011

  27. [27]

    Barrientos and S

    E. Barrientos and S. Mendoza. MOND as the weak field limit of an extended metric theory of gravity with torsion.Eur. Phys. J. Plus, 132(8):361, 2017

    2017

  28. [28]

    M. E. Soussa and Richard P. Woodard. A Generic problem with purely metric formulations of MOND.Phys. Lett. B, 578:253–258, 2004

    2004

  29. [29]

    A closer look at the mond no-go statement for purely metric formulations

    Marc Soussa. A closer look at the mond no-go statement for purely metric formulations. In15th Rencontres de Blois on Physical Cosmology: New Results in Cosmology and the Coherence of the Standard Model, pages 161–164, 2005

    2005

  30. [30]

    MOND as a regime of quantum gravity.Phys

    Lee Smolin. MOND as a regime of quantum gravity.Phys. Rev. D, 96(8):083523, 2017

    2017

  31. [31]

    The modified dynamics as a vacuum effect.Phys

    Mordehai Milgrom. The modified dynamics as a vacuum effect.Phys. Lett. A, 253:273–279, 1999. 11

    1999

  32. [32]

    Pikhitsa

    Peter V. Pikhitsa. MOND reveals the thermodynamics of gravity. 10 2010

    2010

  33. [33]

    V. V. Kiselev and S. A. Timofeev. The Holographic screen at low temperatures.Mod. Phys. Lett. A, 26:109–118, 2011

    2011

  34. [34]

    F. R. Klinkhamer and M. Kopp. Entropic gravity, minimum temperature, and modified Newtonian dynamics.Mod. Phys. Lett. A, 26:2783–2791, 2011

    2011

  35. [35]

    Chiu Man Ho, Djordje Minic, and Y. Jack Ng. Quantum Gravity and Dark Matter.Gen. Rel. Grav., 43:2567–2573, 2011

    2011

  36. [36]

    Pazy and N

    E. Pazy and N. Argaman. Quantum particle statistics on the holographic screen leads to Modified Newtonian Dynamics (MOND).Phys. Rev. D, 85:104021, 2012

    2012

  37. [37]

    Verlinde

    Erik P. Verlinde. Emergent Gravity and the Dark Universe.SciPost Phys., 2(3):016, 2017

    2017

  38. [38]

    Mordehai Milgrom.MOND from a brane-world picture. 2020

    2020

  39. [39]

    The Equivalence Principle and the Emergence of Flat Rotation Curves

    Stephon Alexander and Lee Smolin. The Equivalence Principle and the Emergence of Flat Rotation Curves. 4 2018

    2018

  40. [40]

    Thea0 – cosmology connection in MOND

    Mordehai Milgrom. Thea0 – cosmology connection in MOND. 1 2020

    2020

  41. [41]

    F. I. Cooperstock, V. Faraoni, and D. N. Vollick. The Influence of the cosmological expansion on local systems.Astrophys. J., 503:61, 1998

    1998

  42. [42]

    M. J. Luo. Local Short-Time Acceleration induced Spectral Line Broadening and Possible Implications in Cosmology. Annals of Physics, 473:169899, November 2024

    2024

  43. [43]

    M. J. Luo. Second-order moment quantum fluctuations and quantum equivalence principle.Phys. Lett. A, 535:130273, 2025

    2025

  44. [44]

    M. J. Luo. The cosmological constant problem and re-interpretation of time.Nuclear Physics, 884(1):344–356, 2014

    2014

  45. [45]

    M. J. Luo. Dark energy from quantum uncertainty of distant clock.Journal of High Energy Physics, 06(063):1–11, 2015

    2015

  46. [46]

    M. J. Luo. The cosmological constant problem and quantum spacetime reference frame.Int. J. Mod. Phys., D27(08):1850081, 2018

    2018

  47. [47]

    M. J. Luo. Ricci Flow Approach to The Cosmological Constant Problem.Found. Phys., 51(1):2, 2021

    2021

  48. [48]

    M. J. Luo. Trace anomaly, Perelman’s functionals and the cosmological constant.Class. Quant. Grav., 38(15):155018, 2021

    2021

  49. [49]

    M. J. Luo. Local conformal instability and local non-collapsing in the Ricci flow of quantum spacetime.Annals Phys., 441:168861, 2022

    2022

  50. [50]

    M. J. Luo. A Statistical Fields Theory underlying the Thermodynamics of Ricci Flow and Gravity.Int. J. Mod. Phys. D, 32(5):2350022, 2 2023

    2023

  51. [51]

    M. J. Luo. Quantum Modified Gravity at Low Energy in the Ricci Flow of Quantum Spacetime.Int. J. Theor. Phys., 62(4):91, 2023

    2023

  52. [52]

    M. J. Luo. The Ricci flow and the early universe.Annals of Physics, 458:169452, November 2023

    2023

  53. [53]

    M. J. Luo. Well-posedness of Ricci Flow in Lorentzian Spacetime and its Entropy Formula.arXiv: 2509.17733

    Pith/arXiv arXiv

  54. [54]

    M. J. Luo. Quantum Mechanics Relative to a Quantum Reference System: Relative State Approach.arXiv: 2510.17513

    arXiv

  55. [55]

    Accelerated detectors and temperature in (anti)-de Sitter spaces.Class

    Stanley Deser and Orit Levin. Accelerated detectors and temperature in (anti)-de Sitter spaces.Class. Quant. Grav., 14:L163–L168, 1997

    1997