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arxiv: 1907.09910 · v1 · pith:P6US6RMLnew · submitted 2019-07-17 · ⚛️ physics.gen-ph

Gravitomagnetism and Gravitational Waves in Galileo-Newtonian Physics

Harihar Behera This is my paper

Pith reviewed 2026-05-24 19:58 UTC · model grok-4.3

classification ⚛️ physics.gen-ph
keywords gravitomagnetismgravitational wavesHeaviside-Maxwellian Gravitygravito-Maxwell-Lorentz equationsNewtonian gravityGalileo-Newton relativitygravitostatics
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0 comments X

The pith

Combining static gravity, Galilean relativity, and finite-speed waves yields Maxwell-like equations for gravity.

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

The paper starts from the known laws of gravitostatics and adds the Galileo-Newton principle of relativity plus the assumption that gravitational effects can propagate as waves at finite speed. Using a method parallel to one that derives electromagnetic equations, it obtains two equivalent sets of dynamic equations for gravity. These equations introduce gravitomagnetic fields and gravitational waves into a Galilean-Newtonian setting and fix the wave speed to equal the speed of light. The same framework recovers a correction to an earlier force law and accounts for several effects previously derived only in general relativity.

Core claim

Adopting Schwinger's formalism for inferring Maxwell-Lorentz equations and combining the laws of gravitostatics, the Galileo-Newton principle of relativity and existence of gravitational waves which travel in vacuum with a finite speed c_g, we inferred two sets of gravito-Maxwell-Lorentz Equations (g-MLEs). One of these sets corresponds to Heaviside's Gravity of 1893 and the other set corresponds to what we call Maxwellian Gravity (MG). HG and MG are mere two mathematical representations of a single physical theory called Heaviside-Maxwellian Gravity (HMG). While rediscovering Heaviside's gravitational field equations following Schwinger's formalism, we found a correction to Heaviside's grav

What carries the argument

The gravito-Maxwell-Lorentz equations (g-MLEs) obtained by merging gravitostatics with Galilean relativity and propagating waves; these equations supply the dynamic terms missing from static Newtonian gravity.

If this is right

  • Gravitomagnetic effects and gravitational waves become part of Galilean-Newtonian physics rather than requiring general relativity.
  • The propagation speed of gravitational waves is fixed at the vacuum speed of light.
  • A corrected gravito-Lorentz force law replaces the earlier speculative version.
  • Several experimentally verified general-relativistic results receive explanations inside the new framework.
  • A new but physically equivalent set of Maxwell-Lorentz equations for ordinary electromagnetism is obtained as a byproduct.

Where Pith is reading between the lines

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

  • The same three-ingredient recipe might be tried on other long-range forces to see whether analogous dynamic extensions appear.
  • If the derived equations survive high-precision tests, the classical-relativistic boundary for gravity would need re-examination.
  • The approach supplies a concrete way to search for small deviations from Newtonian gravity that are linear in velocity and acceleration.

Load-bearing premise

Gravitational waves travel through empty space at a finite speed.

What would settle it

Direct measurement showing that changes in gravitational fields propagate at infinite speed, or laboratory data on moving masses that contradict the corrected gravito-Lorentz force law.

read the original abstract

Adopting Schwinger's formalism for inferring Maxwell-Lorentz equations (MLEs) and combining three ingredients: (i) the laws of gravitostatics, (ii) the Galileo-Newton principle of relativity and (iii) existence of gravitational waves which travel in vacuum with a finite speed $c_g$, we inferred two sets of gravito-Maxwell-Lorentz Equations (g-MLEs). One of these sets corresponds to Heaviside's Gravity of 1893 and the other set corresponds to what we call Maxwellian Gravity (MG). HG and MG are mere two mathematical representations of a single physical theory called Heaviside-Maxwellian Gravity (HMG). While rediscovering Heaviside's gravitational field equations following Schwinger's formalism, we found a correction to Heaviside's speculative gravito-Lorentz force law. This work presents a Galilo-Newtonian foundation of gravitomagnetic effects and gravitational waves, caused by time-varying sources and fields, which are currently considered outside the domain of Newtonian physics. The emergence HMG from other well-established principles of physics is also noted, which established its theoretical consistency and fixed the value of $c_g$ uniquely at the speed of light in vacuum. The explanations of certain experimentally verified general relativistic results within HMG are also noted. We also report, a set of new Maxwell-Lorentz Equations, physically equivalent to the standard set, as a byproduct product of the present approach.

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

2 major / 2 minor

Summary. The manuscript adopts Schwinger's formalism to combine gravitostatics, the Galileo-Newton principle of relativity, and the existence of vacuum gravitational waves at finite speed c_g, thereby deriving two equivalent sets of gravito-Maxwell-Lorentz equations (one matching Heaviside 1893 and the other termed Maxwellian Gravity). These are presented as Heaviside-Maxwellian Gravity (HMG), which is claimed to supply a Galilean-Newtonian foundation for gravitomagnetic effects and gravitational waves, to fix c_g uniquely to the speed of light, and to recover certain experimentally verified general-relativistic results.

Significance. If the derivations were free of circularity, the work would supply a concrete illustration of how dynamic gravitational effects can be incorporated into a Newtonian framework while reproducing selected GR phenomenology. The explicit use of Schwinger's method to enforce consistency between static and dynamic sectors is a methodological strength that could be useful for analogous constructions in other field theories.

major comments (2)
  1. [Abstract] Abstract: the assertion that 'the emergence of HMG from other well-established principles of physics ... fixed the value of c_g uniquely at the speed of light in vacuum' is contradicted by the explicit listing of 'existence of gravitational waves which travel in vacuum with a finite speed c_g' as one of the three input ingredients. Because finite propagation speed is presupposed, the subsequent identification c_g = c cannot be derived from gravitostatics or Galilean relativity alone and must be supplied by an additional step that is not among the stated axioms.
  2. [Abstract] Abstract (and the central construction): the inference of the g-MLEs from the three ingredients is described as yielding wave propagation at speed c_g, yet the uniqueness claim for c_g = c rests on the same assumed finite-speed waves; this renders the 'theoretical consistency' argument at least partly tautological and load-bearing for both the Newtonian-foundation claim and the recovery of GR results.
minor comments (2)
  1. [Abstract] Abstract contains the typographical error 'Galilo-Newtonian' (should be 'Galileo-Newtonian') and the redundant phrase 'byproduct product'.
  2. [Abstract] The abstract states that 'a set of new Maxwell-Lorentz Equations, physically equivalent to the standard set' is reported as a byproduct, but no explicit form or section reference is given for these equations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed reading and for highlighting the need for greater precision in the abstract's wording regarding the status of c_g. The comments correctly identify a potential ambiguity in how the input assumptions and derived consistency are presented. We will revise the abstract and relevant sections to clarify the logical structure without altering the manuscript's central claims or derivations.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the assertion that 'the emergence of HMG from other well-established principles of physics ... fixed the value of c_g uniquely at the speed of light in vacuum' is contradicted by the explicit listing of 'existence of gravitational waves which travel in vacuum with a finite speed c_g' as one of the three input ingredients. Because finite propagation speed is presupposed, the subsequent identification c_g = c cannot be derived from gravitostatics or Galilean relativity alone and must be supplied by an additional step that is not among the stated axioms.

    Authors: We accept the referee's observation that the abstract as written can be read as implying that c_g = c follows solely from the first two ingredients. In the manuscript the three ingredients are jointly used within Schwinger's formalism to obtain the g-MLEs; the finite-speed assumption supplies the wave term, while consistency of the resulting equations with gravitostatics and Galilean invariance then requires that the propagation speed equal the electromagnetic c in order for the theory to remain internally consistent and to recover the cited GR limits. The uniqueness is therefore a consequence of the joint application rather than an independent axiom. We will rephrase the abstract to state explicitly that the identification c_g = c is fixed by the consistency requirement imposed by the Schwinger construction. revision: yes

  2. Referee: [Abstract] Abstract (and the central construction): the inference of the g-MLEs from the three ingredients is described as yielding wave propagation at speed c_g, yet the uniqueness claim for c_g = c rests on the same assumed finite-speed waves; this renders the 'theoretical consistency' argument at least partly tautological and load-bearing for both the Newtonian-foundation claim and the recovery of GR results.

    Authors: The input assumption is merely the existence of waves propagating at some finite speed; the Schwinger procedure then produces specific field equations whose wave speed appears as a free parameter. Only the choice c_g = c renders those equations compatible with the static sector and with the Galilean relativity principle while also reproducing the listed GR phenomenology. This supplies a non-trivial constraint rather than a tautology. Nevertheless, we acknowledge that the abstract does not make this logical separation sufficiently clear and will revise the wording to distinguish the input (finite c_g) from the consistency condition that fixes its value. revision: yes

Circularity Check

1 steps flagged

Finite c_g assumed as input ingredient, then claimed fixed to c by consistency with well-established principles

specific steps
  1. fitted input called prediction [Abstract]
    "combining three ingredients: (i) the laws of gravitostatics, (ii) the Galileo-Newton principle of relativity and (iii) existence of gravitational waves which travel in vacuum with a finite speed $c_g$, we inferred two sets of gravito-Maxwell-Lorentz Equations (g-MLEs). ... The emergence HMG from other well-established principles of physics is also noted, which established its theoretical consistency and fixed the value of $c_g$ uniquely at the speed of light in vacuum."

    Ingredient (iii) supplies finite c_g as an input to derive the dynamic equations. The subsequent claim that consistency with well-established principles fixes the value of that same c_g to the speed of light is therefore an identification with external knowledge, not an independent output of the three ingredients. The wave speed in the resulting equations is the input c_g by construction.

full rationale

The paper explicitly lists existence of gravitational waves at finite speed c_g as one of three foundational ingredients used to infer the g-MLEs. It then asserts that emergence from well-established principles establishes consistency and fixes c_g uniquely to the speed of light. This reduces the uniqueness claim to an identification step that matches the input c_g to the known electromagnetic value rather than deriving the numerical value from the other two ingredients alone. The wave equations themselves propagate at the input c_g by construction. No self-citation chain or ansatz smuggling is evident from the provided text; the circularity is confined to this load-bearing identification of the speed value.

Axiom & Free-Parameter Ledger

0 free parameters · 3 axioms · 0 invented entities

The derivation rests on three explicit ingredients plus the implicit assumption that Schwinger's inference procedure applies unchanged to gravity; the wave-speed assumption is the novel addition that enables the dynamic sector.

axioms (3)
  • domain assumption Laws of gravitostatics
    Starting point for inferring the full dynamic equations (abstract).
  • standard math Galileo-Newton principle of relativity
    Physics laws identical in inertial frames; used to constrain the form of the equations.
  • ad hoc to paper Existence of gravitational waves traveling at finite speed c_g in vacuum
    Third ingredient required to obtain time-varying source and field terms.

pith-pipeline@v0.9.0 · 5789 in / 1638 out tokens · 30302 ms · 2026-05-24T19:58:45.416110+00:00 · methodology

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Reference graph

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