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REVIEW 5 major objections 5 minor 12 references

Gravitational friction from d'Alembert's principle

T0 review · 5 major / 5 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read A particle moving at constant velocity through a homogeneous low-density medium loses energy to the medium's gravitational field, with the loss proportional to density and the square of the distance traveled; for photons this appears as a…

desk verdict A cleanly written paper whose central coefficient is inserted by hand; the claimed gravitational friction is not derived. read the letter →

arxiv 2502.07174 v1 pith:O7HM7EON submitted 2025-02-11 physics.class-ph gr-qc

C. Ortiz , R.S. Khatiwada This is my paper · ORCID
classification physics.class-phgr-qc
keywords gravitationalfrictiond'Alembert'sprinciplevirtualworknon-holonomicconstraintsphotonredshiftdissipativemechanicsEuler-Cauchystresshomogeneousmedium
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 tries to establish that the gravitational interaction with a uniform, electrically neutral low-density medium makes any particle moving through it at constant velocity lose energy, even though the medium is symmetric around the particle. Using the principle of virtual work and d'Alembert's principle, which handle the non-holonomic constraint of constant velocity better than least action, the authors derive a total work $W = -\frac{1}{3}\pi G m_0 \rho v_r^2 t^2$ for a particle of mass $m_0$ and, for photons, $W = -\frac{1}{3c}\pi G p \rho r^2$. The negative sign is time-accumulating, so the effect is dissipative and irreversible. If correct, this is a previously unidentified energy-loss channel that acts independently of scattering, and for photons it would contribute a redshift that grows with the density of the medium and the square of the distance traveled.

What carries the argument

The load-bearing object is the d'Alembert principle—a formulation that adds an inertial force so a moving system can be treated as static—used together with the principle of virtual work under the non-holonomic constraint $g(r,v,t)=r-vt=0$. The key step is converting the infinite plane's surface density $\sigma$ into a volume density through $\sigma = \rho r/3$, described as projecting the volume of a cone into a circle; this turns the constant plane force $F_r=-2\pi G m_0 \sigma$ into the time-growing force $F_r=-\frac{2}{3}\pi G m_0 \rho v_r t$. The alternative route uses the Euler-Cauchy stress principle applied to a half-sphere, with the gravitational potential treated as a non-polar surface tension, which yields the same energy loss.

What would settle it

Do a direct numerical integration of the Newtonian $1/r^2$ gravitational force on a test particle from a uniform medium inside a large sphere centered on the particle: symmetry makes the net force zero, whereas Eq. (7) predicts $F_r=-\frac{2}{3}\pi G m_0 \rho v_r t$, which grows without bound; the two results cannot both be right.

Watch

Extended reading notes

Core claim

The paper's central claim is that gravitational interaction with a uniform medium is intrinsically dissipative for any particle forced to move at constant velocity. Applying d'Alembert's principle to the non-holonomic constraint $g(r,v,t)=r - v t = 0$, the authors find that the reaction of the medium produces a force $F_r = -\frac{2}{3}\pi G m_0 \rho v_r t$ and hence a power $dW/dt = -\frac{2}{3}\pi G m_0 \rho v_r^2 t \leq 0$. Integrating over the traversal gives $W = -\frac{1}{3}\pi G m_0 \rho v_r^2 t^2 = -\frac{1}{3}\pi G m_0 \rho r^2$. For photons, replacing the particle mass by momentum $p$ through the plane-wave relation gives $W = -\frac{1}{3c}\pi G p \rho r^2$, which corresponds to a fractional energy loss $\Delta E/E = -\pi G \rho r^2/(3 c^2)$ and therefore a redshift. The same energy expression is obtained independently from a continuum-mechanics surface-tension argument based on the Euler-Cauchy stress principle, which the authors take as mutual confirmation.

Load-bearing premise

The whole quantitative result hangs on the assumption that a cone of the medium can be flattened into a circle with surface density $\sigma=\rho r/3$; nothing in the physics dictates that cone, so changing this geometric identification changes the coefficient and hence the predicted magnitude.

Editorial extensions

If this is right

  • Every particle forced to move at constant speed through a uniform medium loses energy to gravity, with $W=-\frac{1}{3}\pi G m_0 \rho r^2$ after traversing a distance $r$.
  • Photons suffer a fractional energy loss $\Delta E/E = -\pi G \rho r^2/(3c^2)$, giving an irreversible redshift that accumulates with distance and density.
  • Because the power $dW/dt$ is negative at all times, the mechanism can never blueshift a photon, ruling out blueshifts from this channel.
  • The effect is independent of scattering and other loss mechanisms, which is why the authors propose that a long-baseline low-density interferometer could isolate it.
  • The same energy expression is recovered from the Euler-Cauchy stress principle, giving the result two independent derivations.

Reading between the lines

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

  • Editorial extension: the coefficient $1/3$ is fixed by the cone-projection assumption, so a decisive test should look for the predicted $\rho r^2$ scaling rather than treat the prefactor as exact.
  • Editorial extension: applied to a roughly constant-density intergalactic medium, the formula implies a redshift contribution growing as the square of the distance, which would look like a distance-dependent drift; the paper does not quantify this cosmological consequence.
  • Editorial extension: an interferometer experiment with variable gas density could separate the effect from refractive-index changes by checking whether any residual fringe shift is linear in density and quadratic in arm length.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

5 major / 5 minor

Summary. The manuscript claims to derive a new dissipative mechanism, 'gravitational friction,' using the d'Alembert principle and the principle of virtual work. The central result is Eq. (10), which gives the energy lost by a particle moving at constant velocity through a homogeneous medium as W = -(1/3)πGm₀ρv_r²t², and Eq. (16), which extends this to photons by replacing m₀ with p/c, yielding a gravitational redshift. An alternative derivation based on the Euler-Cauchy stress principle is presented as confirmation, and a LIGO-based experiment is proposed to test the effect.

Significance. If the claimed effect were real, it would be a novel energy-loss mechanism with consequences for the motion of particles in low-density media and for the redshifts of electromagnetic waves. The paper correctly reproduces the standard result for the gravitational field of an infinite uniform sheet (Eq. 6). However, the key step that makes the force distance-dependent is an ad hoc geometrical assumption, and the alternative derivation repeats the same coefficient rather than providing an independent check. The central quantitative claim is therefore not established, and the proposed experimental test is not quantitatively developed. The paper's strengths are confined to the standard infinite-plane calculation and the identification that constant-velocity constraints are best handled with d'Alembert's principle.

major comments (5)
  1. [Gravitational friction, between Eqs. (6) and (7)] The step σ = ρr/3 is an assumption, not a consequence of the geometry or of any physical principle. The force from an infinite plane is independent of distance (Eq. 6), so the r-dependence in Eq. (7) is injected entirely by this geometric ansatz. A cylinder projection, for example, would give a different coefficient, so the factor 1/3 in Eq. (10) is not fixed by the stated principles. This makes the quantitative prediction arbitrary and the claim of a first-principles derivation untenable.
  2. [Gravitational friction, Eqs. (7)–(10)] The work calculation conflates the position variable r with the displacement used to compute work. Equation (7) substitutes r = v_r t into the force, so Fr is evaluated at the current position; integrating Fr dr with dr = v_r dt then yields a result proportional to r² because the force itself was made proportional to r. A consistent treatment would derive the force on a moving particle from the medium's density distribution and then integrate the work along the path; the present derivation does not do so, and the r² dependence is therefore an artifact of the assumptions.
  3. [Photons in low density medium, Eq. (16)] The substitution m₀ → p/c is unjustified. Equation (10) is derived for a massive test particle whose gravitational mass m₀ enters Newton's force law. A photon has no rest mass, and its interaction with gravitational fields is governed by general relativity, not by the Newtonian formula with a mass proxy. No physical argument is given for why the Newtonian work expression should apply to photons with this substitution, so the gravitational redshift formula is unsupported.
  4. [Gravitational Surface Tension, Eqs. (12)–(15)] The Euler-Cauchy stress-principle derivation is not independent and is not physically justified. The 'surface tension' γ_s is introduced as FS/(2R), then Eq. (13) identifies FS with the gravitational force on a point mass without derivation, and Eq. (14) uses M = (2/3)πρr³, a half-sphere volume that already contains the factor 1/3. The agreement between Eq. (15) and Eq. (10) therefore reflects the repeated use of the same 1/3 coefficient, not confirmation by an independent method. The identification of gravitational potential energy with surface tension is also not explained.
  5. [Gravitational friction, Eq. (9)] The dissipativity claim is not established. The gravitational interaction is conservative; the negative work done on the particle is equal to the increase in the potential energy of the particle–medium system. For the constant-velocity constraint to hold, an external agent must supply the energy lost by the particle, and the paper neither models nor discusses this energy balance. Labeling the effect as 'friction' therefore exceeds what the calculation actually shows.
minor comments (5)
  1. [Introduction] The paper repeatedly states that the constraint is non-holonomic and that this motivates the use of d'Alembert's principle, but the constraint g(r, v, t) = r − vt = 0 is a time-dependent holonomic constraint, not a non-holonomic one. This error in the framing should be corrected.
  2. [Throughout] There are typographical and notation inconsistencies, such as 'd’Alembert' vs 'D'Alembert' and 'vz' vs 'v_r' near Eq. (10); the manuscript should be carefully edited.
  3. [Figure 1] Figure 1 is not included in the manuscript, so the 'configuration of the displacement' that motivates the cone projection is not visually defined.
  4. [Discussion] The proposed LIGO test is not quantitatively assessed; no estimate is given for the magnitude of the predicted energy loss in a realistic vacuum, so the feasibility of the test is unclear.
  5. [References] The relation of the present work to the author's previous paper (Ref. 8) should be clarified, and the manuscript does not engage with the standard literature on dynamical friction, which would provide a necessary context for the claimed mechanism.

Circularity Check

2 steps flagged · score 6.0 of 10

The central 1/3 coefficient is inserted by the cone ansatz σ=ρr/3, and the stress-based 'confirmation' reuses the same geometric factor plus a self-cited hypothesis, so Eq. (10) is not independently derived.

  1. other [Gravitational friction, between Eqs. (6) and (7)]
    "Since we are dealing with a virtual displacement away from the surface, the surface density, σ, must be expressed in terms of the volume density, ρ, M = σA = ρV. Given the configuration of the displacement, see Figure 1, we assume the volume of a cone projected into a circle, hence σ = ρr/3."

    Equation (6) gives the force of an infinite plane as Fr = -2πGm0σ, which is independent of distance. The r-dependence and the 1/3 coefficient of the central result (10) enter only through this assumed σ = ρr/3. Substituting into (6) and integrating dW = Fr v_r dt gives W = -(1/3)πGm0ρv_r²t², so Eq. (10) is an algebraic restatement of the conical-projection ansatz rather than a prediction derived from d'Alembert's principle.

  2. self citation load bearing [Gravitational Surface Tension, before Eq. (11) and Eq. (14)]
    "Therefore, as part of our hypothesis, we introduce the gravitational potential in the surface tension relation. ... We must acknowledge that the aforementioned hypothesis was previously developed in a general relativistic context8, with a different setup. ... The mass is related to the density of the half-sphere, M = (2/3)πρ r3."

    The claimed independent confirmation via the Euler-Cauchy stress principle is not independent: it rests on the surface-tension hypothesis taken from the same author's prior work (ref. 8), and it obtains the same 1/3 coefficient by choosing M = (2/3)πρr³ for a half-sphere. This is the same geometric factor that entered through σ = ρr/3 in the first derivation; hence Eq. (15) reproducing Eq. (10) is agreement of two formulations of the same input, not a corroboration from outside the paper's assumptions.

full rationale

The paper's central quantitative claim, Eq. (10), is not derived from first principles in a way that determines its magnitude. The force of an infinite uniform plane, Eq. (6), is independent of r; all r-dependence and the 1/3 prefactor in Eq. (10) are inserted by the explicit assumption σ = ρr/3, justified only by 'we assume the volume of a cone projected into a circle.' The second derivation, presented as an independent check, uses the same geometric factor through the half-sphere mass M = (2/3)πρr³, so its agreement with Eq. (10) is by construction rather than by independent physics. This second derivation also explicitly imports a surface-tension hypothesis previously developed by the same author in ref. 8, making the self-citation load-bearing for the claimed confirmation. There is no external benchmark, data fit, or externally constrained parameter that fixes the 1/3 coefficient; changing the projection geometry would change the predicted magnitude. The existence of a nonzero plane force is not circular, but the specific predicted energy loss reduces to the assumed geometric input, giving a score of 6 rather than a clean non-finding.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central claim rests entirely on the assumed cone projection factor (1/3) and on the unphysical extension to photons via m0 = p/c. No data are used. The paper's two derivations share the same geometric assumption, so the agreement is expected. The constraint g = r - vt = 0 is holonomic, despite the paper's non-holonomic framing.

free parameters (2)
  • cone projection factor (1/3) in σ = ρr/3 = 1/3
    The only numerical parameter in the central result. It arises from assuming the displaced mass is a cone projected onto a circle (σ = ρr/3). No physical principle fixes this factor; choosing a cylinder gives σ = ρr and changes the coefficient in Eq. (10).
  • photon mass proxy p/c = p/c
    For photons, m0 is replaced by p/c in Eq. (10) to obtain Eq. (16). This is an ad hoc substitution, not derived from electrodynamics or general relativity.
assumptions (4)
  • domain assumption The net gravitational force on the test particle from the homogeneous medium reduces to the force from an infinite plane; contributions from the two half-spaces cancel exactly.
    Section 'Gravitational friction': 'Due to the symmetry of the configuration, the force on a particle due to the matter content in the upper region, Ω+, is canceled out by the force due to the one in the lower region, Ω−.' Assumes strict homogeneity and exact symmetry about the plane.
  • ad hoc to paper The surface density of the plane is related to the volume density by σ = ρr/3 from the cone projection assumption.
    Introduced as 'we assume the volume of a cone projected into a circle'. This geometric factor is chosen without derivation and directly controls the final energy loss, propagating through Eqs. (7)-(10) and (16).
  • ad hoc to paper Photons can be treated as massive particles with mass m0 replaced by p/c and velocity c in the Newtonian energy-loss formula.
    Section 'Photons in low density medium': 'By considering the momentum of the photon, denoted as p, we can reframe Equation (10) as follows.' No derivation is provided for this substitution.
  • domain assumption The Euler-Cauchy stress principle applies with a gravitational surface tension γ_s = F_s/(2R), and the mass of the half-sphere is M = (2/3)πρr³.
    Section 'Gravitational Surface Tension': 'as part of our hypothesis, we introduce the gravitational potential in the surface tension relation.' The agreement with Eq. (10) uses the same spherical mass scaling and is not an independent check.

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Cite this review

Pith. "Pith review of Gravitational friction from d'Alembert's principle." pith.science (2026). https://pith.science/paper/O7HM7EON

@misc{pith2026250207174,
  author       = {Pith},
  title        = {Pith review of: Gravitational friction from d'Alembert's principle},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/O7HM7EON}},
  note         = {Machine review of arXiv:2502.07174}
}
read the original abstract

The least action principle played a central role in the development of modern physics. A major drawback of the principle is that its applicability is limited to holonomic constraints. In the present work, we investigate the energy lost by particles as a result of the gravitational interaction in a homogeneous low-density medium subject to non-holonomic constraints. We perform the calculation for an arbitrary particle and outline the specific result for photons. The energy lost is calculated from first principles based on the principle of virtual work and the d'Alembert principle. Under the formalism mentioned above, the dissipative nature of the effect is established. Furthermore, we show that the results agree with an alternative derivation based on continuum mechanics and the Euler-Cauchy stress principle.

Figures

Figures reproduced from arXiv: 2502.07174 by the authors.

Figure 1
Figure 1. Geometrical configuration of the system Since we are dealing with a virtual displacement away from the surface, the surface density, σ, must be expressed in terms of the volume density, ρ, M = σA = ρV. Given the configuration of the displacement, see [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

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