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{{Infobox paper | {{Infobox paper | ||
| title = Gravitation - A New Theory. Generation of the Gravitational Acceleration Potential and The Time | | title = Gravitation - A New Theory. Generation of the Gravitational Acceleration Potential and The Time | ||
Dilatation Effect | Dilatation Effect | ||
| url = [http://www.naturalphilosophy.org/pdf/abstracts/abstracts_799.pdf Link to paper] | | url = [http://www.naturalphilosophy.org/pdf/abstracts/abstracts_799.pdf Link to paper] | ||
| author = [[Peter G Bass]] | | author = [[Peter G Bass]] | ||
| Line 7: | Line 7: | ||
| published = 2004 | | published = 2004 | ||
| journal = [[Apeiron]] | | journal = [[Apeiron]] | ||
| volume = | | volume = 11 | ||
| number = | | number = 1 | ||
| num_pages = | | num_pages = 32 | ||
}} | }} | ||
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==Abstract== | ==Abstract== | ||
Following the presentation of the new theory of gravitation in [1], this paper presents a mathematical derivation for the generation by the gravitational source, of the two central parameters in that theory, gravitational Acceleration Potential and the time dilatation effect. | |||
</ | ''Keywords'': Gravitation, Relativity, Special, General, Minkowski, Space-Time, Temporal, Acceleration, Potential, Time, Dilatation. | ||
==Overview== | |||
Peter G. Bass, a retired project manager writing from Watford, England, published this paper in ''[[Apeiron]]'' in January 2004 as the third instalment of his "Relativistic Domain Theory". It follows [[Gravitation - A New Theory]] (''Apeiron'' 10(4), 98–151) and [[Gravitation - A New Theory. Further Kinetics of Gravitational Motion]] (''Apeiron'' 11(1), 187–212), and assumes familiarity with both, together with his classical treatment of special relativity in the same journal. | |||
Bass's complaint against [[General Relativity]] is not that it fails observationally but that it explains nothing physically: curvature of space-time is said to be caused by ponderable matter, yet "the precise mechanism that causes this space-time distortion by the source is not described", and the characteristics a continuum would need in order to be so distorted are never addressed. Only the geometry — the geodesics — is given. In his alternative, the Relativistic Space-Time Domain ''D''<sub>1</sub>, space-time is '''not curved but completely linear along all four axes''', while still exhibiting (he claims in [1]) identical gravitational characteristics to General Relativity. Motion is instead caused by an "Acceleration Potential" existing within the Domain, augmented by the time dilatation the source produces. This paper asks how a mass ''generates'' those two quantities. Its answer: the source converts temporal motion into a radial expansion of space itself, and the small "velocity of space" so produced accounts for both effects at once. Bass is explicit and repeated in warning that this is speculative — the proposed direct relationship between space, time and matter has no observational or experimental support, and no clear route to testing it. | |||
==The argument== | |||
===How time is generated in a Domain=== | |||
In the field-free Domain ''D''<sub>0</sub> (pseudo-Euclidean space-time) all points move along the temporal axis at velocity ''c'', and an elemental temporal distance Δ''x''<sub>0</sub> produces an element of time Δ''t'' = Δ''x''<sub>0</sub>/''c'' in the spatial dimensions. In the gravitational Domain ''D''<sub>1</sub> the temporal velocity is ''cu'', so Δτ = Δ''x''<sub>0</sub>/''cu'', giving Δτ/Δ''t'' = 1/''u''. Since ''u'' < 1, an element of time in ''D''<sub>1</sub> is longer, so time passes more slowly there: 1 second in ''D''<sub>1</sub> ≡ ''u'' seconds in ''D''<sub>0</sub>, and ''d''τ/''dt'' = ''u''. The parameter ''u'', called the Temporal Rate, is thus the whole of [[Time Dilation]] in this scheme. | |||
Bass then revises the notion of "temporal velocity". If different spatial points moved at different speeds along the temporal axis they would drift apart on it — "equivalent to 'travelling in time' which is obviously not within observed experience". He replaces it with '''temporal flow''': the temporal dimension moves past a single three-dimensional "plane of existence" on which all matter co-exists, arriving from the future at constant velocity ''c'' and leaving toward the past at the reduced, position-dependent velocity ''cu''. Every body stays on one plane while still experiencing a spatially varying rate of time. | |||
===Three candidate mechanisms, two rejected=== | |||
Outside the source, Bass's earlier paper gives ''u'' = (1 − α/σ)<sup>1/2</sup> with α the gravitational radius and σ the radial distance. He argues the variability of Δτ = Δ''x''<sub>0</sub>/''cu'' can arise in only three ways: (i) temporal velocity ''cu'' is directly reduced by an interaction between source and continuum; (ii) the temporal distance Δ''x''<sub>0</sub> is stretched, simulating a velocity reduction; or (iii) the source generates a small ''spatial'' velocity along all radius vectors, which via the Domain's "criterion of existence" reduces the temporal velocity. | |||
He rejects (i) on two grounds: a temporal forcing function applied to a mass would change its ''mass'' rather than its temporal velocity — a claim he states "without proof", deferring it to a future paper — and outside the source there is nothing material for a temporal resistive force to act on. He rejects (ii) because his earlier results were all obtained by attaching ''u'' to the velocity ''c'' rather than to the increment Δ''x''<sub>0</sub>, and again because it is unclear how the stretching would extend beyond the source. Option (iii) survives by elimination. | |||
===Space as a wavefront expanding out of the temporal axis=== | |||
Writing ''u'' = (1 − ''v''<sub>σ</sub><sup>2</sup>/''c''<sup>2</sup>)<sup>1/2</sup> and equating it to (1 − α/σ)<sup>1/2</sup> gives directly ''v''<sub>σ</sub> = (γ''m''<sub>g</sub>/σ)<sup>1/2</sup> — but Bass regards this as a result without a mechanism. Since ''v''<sub>σ</sub> must exist along every radius vector, it cannot belong to the source's matter; the only remaining carrier is "the very fabric of space". He proposes that as the source moves along the temporal axis, a transition occurs from the temporal to the spatial dimensions, expanding space outward from the source's centre as "an infinitely close series of spherical spatial wavefronts". Notably, he argues the process consumes no energy: space is not a distributed energy field, no energy-conversion derivation of the effect could be constructed, and so the expansion is "governed only by its temporal motion". | |||
===Deriving the expansion velocity=== | |||
The derivation's pivot is dimensional. The constant γ has units (length)<sup>4</sup>/(time)<sup>2</sup>(force) per unit mass, so any product γ(mass) has units (length)<sup>3</sup>/(time)<sup>2</sup> — a '''second-order rate of change of volume'''. Outside the source, with mass effectively constant, Bass writes ''d''<sup>2</sup>''W''/''d''τ<sup>2</sup> = ''K''<sub>0</sub>γ''m''<sub>g</sub> for the generated volume ''W'' = (4π/3)(σ<sup>3</sup> − σ<sub>g</sub><sup>3</sup>). Expanding, substituting the known Acceleration Potential ''d''<sup>2</sup>σ/''d''τ<sup>2</sup> = −γ''m''<sub>g</sub>/σ<sup>2</sup>, differentiating again and re-substituting fixes the constant at ''K''<sub>0</sub> = 12π and returns exactly | |||
: ''v''<sub>σ</sub> = ''d''σ/''d''τ = (2γ''m''<sub>g</sub>/σ)<sup>1/2</sup> | |||
whose time derivative is the Acceleration Potential and which, through ''u'' = (1 − ''v''<sub>σ</sub><sup>2</sup>/''c''<sup>2</sup>)<sup>1/2</sup>, reproduces the external time dilatation. | |||
Inside the source the right-hand side is an unknown function f(); using ''a''<sub>int</sub> = −γ''m''<sub>g</sub>σ<sub>i</sub>/σ<sub>g</sub><sup>3</sup> (the standard shell result for a uniform sphere) a linear first-order equation in f() is obtained, solved with integrating factor 1/σ<sub>i</sub>, and the constant of integration fixed by matching ''v''<sub>σ</sub> at the surface σ<sub>i</sub> = σ<sub>g</sub>. The internal expansion velocity is | |||
: ''v''<sub>iσ</sub> = (3γ''m''<sub>g</sub>/σ<sub>g</sub> − γ''m''<sub>g</sub>σ<sub>i</sub><sup>2</sup>/σ<sub>g</sub><sup>3</sup>)<sup>1/2</sup> | |||
giving ''u''<sub>i</sub> = (1 − 3α/σ<sub>g</sub> + ασ<sub>i</sub><sup>2</sup>/σ<sub>g</sub><sup>3</sup>)<sup>1/2</sup>. There is no discontinuity at the boundary. At the very centre ''u''<sub>i</sub> = (1 − 3α/σ<sub>g</sub>)<sup>1/2</sup>, which Bass notes "has implications regarding a limiting value for σ<sub>g</sub>" — his analogue of a collapse limit — deferred to a later paper. | |||
===Field equations=== | |||
Defining ''U''<sub>σ</sub> = ''v''<sub>σ</sub><sup>2</sup>/2 = (''c''<sup>2</sup>/2)(1 − ''u''<sup>2</sup>), Bass obtains ∂''U''<sub>σ</sub>/∂σ = −γ''m''<sub>g</sub>/σ<sup>2</sup> and hence ∇<sup>2</sup>''U''<sub>σ</sub> = 0 outside the source and ∇<sup>2</sup>''U''<sub>iσ</sub> = −4πγρ<sub>g</sub> inside — Laplace's and Poisson's equations. The Acceleration Potential is a gradient field and therefore irrotational, ∇ × '''A'''<sub>σ</sub> = 0, both inside and out. Comparing with the Newtonian potential ''U'' = γ''m''<sub>g</sub>/''r'' gives ''U''<sub>σ</sub>/''U'' = ''r''/σ, so "the only difference between the Newtonian and Relativistic Domain gravitational potentials is a relativistic one" — an expected consequence of ''D''<sub>1</sub> being a linear continuum. | |||
===Physical picture and consequences=== | |||
The expansion enters the spatial dimensions at the source's centre with the velocity given by the constant term of ''v''<sub>iσ</sub>, is decelerated inside the body by an apparent "spatial re-absorption" represented by the variable term, and beyond the surface is attenuated only by the inverse-distance dependence. Bass notes the negative roots of ''v''<sub>σ</sub> and ''v''<sub>iσ</sub> are equally valid solutions, describing a ''contraction'' of space and hence negative gravitation, whose importance he reserves for a promised cosmological paper. Because the expansion carries no energy it can exert no mechanical force: it "would simply flow past and through" other bodies. The only two effects on a nearby body are the negative acceleration from the Acceleration Potential and a smaller, velocity-dependent positive acceleration arising from motion through the varying temporal rate. One testable-sounding consequence is offered: since re-absorption occurs inside matter, the combined gravitational effect behind two aligned bodies "would be very slightly less than the sum of their individual gravitational potentials" — a shielding prediction. An appendix relates the ''D''<sub>1</sub> and ''D''<sub>0</sub> radial coordinates as σ = ''r''(1 − ''v''<sub>σ</sub><sup>2</sup>/2''c''<sup>2</sup>)<sup>−1</sup>, and shows σ<sub>i</sub> = 0 when ''r''<sub>i</sub> = 0. | |||
==Assessment== | |||
What is genuinely attractive here is the ambition to supply a ''mechanism'' where the standard account supplies only geometry, and the honesty with which Bass labels the speculative parts. He does not claim experimental support; he says plainly that none exists and that he cannot see how to obtain it. The internal-solution derivation is careful about continuity: the boundary condition at σ<sub>i</sub> = σ<sub>g</sub> is imposed explicitly rather than assumed, the internal and external potentials match, and the recovery of Laplace and Poisson equations with an irrotational field is a real consistency check rather than decoration. The dimensional observation that γ(mass) has the units of a second time-derivative of volume is a neat piece of physical reading, and it is the one place in the paper where the expansion hypothesis looks motivated rather than merely permitted. That ''v''<sub>σ</sub> = (2γ''m''/σ)<sup>1/2</sup> is the Newtonian escape velocity is also suggestive — the same quantity appears in the Gullstrand–Painlevé "river" form of the Schwarzschild metric, so Bass's picture of space flowing radially is not an idle analogy, and readers of that literature will find the result familiar. | |||
The difficulties are serious. Most of the paper is not a derivation of the expansion hypothesis but a demonstration that it can be made ''consistent'' with results already established in [1]. The key step in Section 3.3.2 inserts the previously known Acceleration Potential ''d''<sup>2</sup>σ/''d''τ<sup>2</sup> = −γ''m''<sub>g</sub>/σ<sup>2</sup> into the volume equation, differentiates, and re-inserts the same relation to fix ''K''<sub>0</sub> = 12π. The answer ''v''<sub>σ</sub> = (2γ''m''<sub>g</sub>/σ)<sup>1/2</sup> was already obtained trivially in Eq. (3.9) by equating (3.3) and (3.8); the longer route recovers it because it was fed in. ''K''<sub>0</sub> is thereby fitted, not predicted, and the "second-order rate of change of volume" premise does no independent work. | |||
The elimination argument that establishes mechanism (iii) is weaker than the mathematics it supports. Only three possibilities are entertained, with no argument that the list is exhaustive; option (i) is discarded partly on a claim "stated here without proof" and deferred to an unwritten paper; and both rejections lean on the same objection — that the effect must also exist outside the source — which mechanism (iii) meets only by asserting that space itself flows, an assumption at least as strong as the ones being rejected. The energy argument is likewise assertive: the conclusion that the process consumes no energy rests in part on the author's inability to construct a derivation in which it does. | |||
Against measurement, the paper's position is unclear because it defers the comparison to [1]. The claim that ''D''<sub>1</sub> reproduces General Relativity's gravitational characteristics is asserted, not shown here, and the results in this paper reproduce the ''Newtonian'' potential to first order with a relativistic correction of unspecified order. The paper never confronts the classical tests that discriminate at that order — the 43″/century anomalous perihelion advance of Mercury, the 1.75″ deflection of starlight at the solar limb (twice the Newtonian value), or the Shapiro delay — nor the Hulse–Taylor binary pulsar's orbital decay, which is a direct probe of a ''non-linear'' field theory with quadrupole radiation. A continuum that is "completely linear along all four axes" has no obvious mechanism for gravitational radiation at all, and the direct detection of [[Gravitational Waves]] a decade after publication makes that omission consequential. The internal solution's central value ''u''<sub>i</sub> = (1 − 3α/σ<sub>g</sub>)<sup>1/2</sup> is, notably, the same limit as the interior Schwarzschild (Buchdahl) bound, but Bass flags it without exploring whether it agrees for the same reason. | |||
Finally, the shielding prediction — a slight deficit behind two aligned bodies due to "re-absorption" — is the one place the theory offers something a measurement could settle, and it is exactly here that the paper offers no magnitude. Absorption-type gravity of this kind is tightly constrained by lunar and solar eclipse gravimetry and by the absence of anomalous heating in massive bodies (the classical objection to Le Sage-type [[Push Gravity]]); without a number the claim cannot be assessed. On its own terms the mathematics is competent and internally consistent, but the paper establishes compatibility rather than support, and Bass says as much in his concluding remarks, where the strongest evidence he claims is "circumstantial". | |||
==See also== | |||
* [[Peter G Bass]] | |||
* [[Gravitation - A New Theory]] | |||
* [[Gravitation - A New Theory. Further Kinetics of Gravitational Motion]] | |||
* [[General Relativity]] | |||
* [[Special Relativity]] | |||
* [[Time Dilation]] | |||
* [[Gravity]] | |||
* [[Equivalence Principle]] | |||
* [[Push Gravity]] | |||
[[Category:Scientific Paper|gravitation - new theory generation gravitational acceleration potential time dilatation effect]] | [[Category:Scientific Paper|gravitation - new theory generation gravitational acceleration potential time dilatation effect]] | ||
| Line 25: | Line 95: | ||
[[Category:Time]] | [[Category:Time]] | ||
[[Category:Gravity]] | |||
Latest revision as of 09:49, 21 July 2026
| Scientific Paper | |
|---|---|
| Title | Gravitation - A New Theory. Generation of the Gravitational Acceleration Potential and The Time Dilatation Effect |
| Read in full | Link to paper |
| Author(s) | Peter G Bass |
| Keywords | Time, Dilatation |
| Published | 2004 |
| Journal | Apeiron |
| Volume | 11 |
| Number | 1 |
| No. of pages | 32 |
Read the full paper here
Abstract
Following the presentation of the new theory of gravitation in [1], this paper presents a mathematical derivation for the generation by the gravitational source, of the two central parameters in that theory, gravitational Acceleration Potential and the time dilatation effect.
Keywords: Gravitation, Relativity, Special, General, Minkowski, Space-Time, Temporal, Acceleration, Potential, Time, Dilatation.
Overview
Peter G. Bass, a retired project manager writing from Watford, England, published this paper in Apeiron in January 2004 as the third instalment of his "Relativistic Domain Theory". It follows Gravitation - A New Theory (Apeiron 10(4), 98–151) and Gravitation - A New Theory. Further Kinetics of Gravitational Motion (Apeiron 11(1), 187–212), and assumes familiarity with both, together with his classical treatment of special relativity in the same journal.
Bass's complaint against General Relativity is not that it fails observationally but that it explains nothing physically: curvature of space-time is said to be caused by ponderable matter, yet "the precise mechanism that causes this space-time distortion by the source is not described", and the characteristics a continuum would need in order to be so distorted are never addressed. Only the geometry — the geodesics — is given. In his alternative, the Relativistic Space-Time Domain D1, space-time is not curved but completely linear along all four axes, while still exhibiting (he claims in [1]) identical gravitational characteristics to General Relativity. Motion is instead caused by an "Acceleration Potential" existing within the Domain, augmented by the time dilatation the source produces. This paper asks how a mass generates those two quantities. Its answer: the source converts temporal motion into a radial expansion of space itself, and the small "velocity of space" so produced accounts for both effects at once. Bass is explicit and repeated in warning that this is speculative — the proposed direct relationship between space, time and matter has no observational or experimental support, and no clear route to testing it.
The argument
How time is generated in a Domain
In the field-free Domain D0 (pseudo-Euclidean space-time) all points move along the temporal axis at velocity c, and an elemental temporal distance Δx0 produces an element of time Δt = Δx0/c in the spatial dimensions. In the gravitational Domain D1 the temporal velocity is cu, so Δτ = Δx0/cu, giving Δτ/Δt = 1/u. Since u < 1, an element of time in D1 is longer, so time passes more slowly there: 1 second in D1 ≡ u seconds in D0, and dτ/dt = u. The parameter u, called the Temporal Rate, is thus the whole of Time Dilation in this scheme.
Bass then revises the notion of "temporal velocity". If different spatial points moved at different speeds along the temporal axis they would drift apart on it — "equivalent to 'travelling in time' which is obviously not within observed experience". He replaces it with temporal flow: the temporal dimension moves past a single three-dimensional "plane of existence" on which all matter co-exists, arriving from the future at constant velocity c and leaving toward the past at the reduced, position-dependent velocity cu. Every body stays on one plane while still experiencing a spatially varying rate of time.
Three candidate mechanisms, two rejected
Outside the source, Bass's earlier paper gives u = (1 − α/σ)1/2 with α the gravitational radius and σ the radial distance. He argues the variability of Δτ = Δx0/cu can arise in only three ways: (i) temporal velocity cu is directly reduced by an interaction between source and continuum; (ii) the temporal distance Δx0 is stretched, simulating a velocity reduction; or (iii) the source generates a small spatial velocity along all radius vectors, which via the Domain's "criterion of existence" reduces the temporal velocity.
He rejects (i) on two grounds: a temporal forcing function applied to a mass would change its mass rather than its temporal velocity — a claim he states "without proof", deferring it to a future paper — and outside the source there is nothing material for a temporal resistive force to act on. He rejects (ii) because his earlier results were all obtained by attaching u to the velocity c rather than to the increment Δx0, and again because it is unclear how the stretching would extend beyond the source. Option (iii) survives by elimination.
Space as a wavefront expanding out of the temporal axis
Writing u = (1 − vσ2/c2)1/2 and equating it to (1 − α/σ)1/2 gives directly vσ = (γmg/σ)1/2 — but Bass regards this as a result without a mechanism. Since vσ must exist along every radius vector, it cannot belong to the source's matter; the only remaining carrier is "the very fabric of space". He proposes that as the source moves along the temporal axis, a transition occurs from the temporal to the spatial dimensions, expanding space outward from the source's centre as "an infinitely close series of spherical spatial wavefronts". Notably, he argues the process consumes no energy: space is not a distributed energy field, no energy-conversion derivation of the effect could be constructed, and so the expansion is "governed only by its temporal motion".
Deriving the expansion velocity
The derivation's pivot is dimensional. The constant γ has units (length)4/(time)2(force) per unit mass, so any product γ(mass) has units (length)3/(time)2 — a second-order rate of change of volume. Outside the source, with mass effectively constant, Bass writes d2W/dτ2 = K0γmg for the generated volume W = (4π/3)(σ3 − σg3). Expanding, substituting the known Acceleration Potential d2σ/dτ2 = −γmg/σ2, differentiating again and re-substituting fixes the constant at K0 = 12π and returns exactly
- vσ = dσ/dτ = (2γmg/σ)1/2
whose time derivative is the Acceleration Potential and which, through u = (1 − vσ2/c2)1/2, reproduces the external time dilatation.
Inside the source the right-hand side is an unknown function f(); using aint = −γmgσi/σg3 (the standard shell result for a uniform sphere) a linear first-order equation in f() is obtained, solved with integrating factor 1/σi, and the constant of integration fixed by matching vσ at the surface σi = σg. The internal expansion velocity is
- viσ = (3γmg/σg − γmgσi2/σg3)1/2
giving ui = (1 − 3α/σg + ασi2/σg3)1/2. There is no discontinuity at the boundary. At the very centre ui = (1 − 3α/σg)1/2, which Bass notes "has implications regarding a limiting value for σg" — his analogue of a collapse limit — deferred to a later paper.
Field equations
Defining Uσ = vσ2/2 = (c2/2)(1 − u2), Bass obtains ∂Uσ/∂σ = −γmg/σ2 and hence ∇2Uσ = 0 outside the source and ∇2Uiσ = −4πγρg inside — Laplace's and Poisson's equations. The Acceleration Potential is a gradient field and therefore irrotational, ∇ × Aσ = 0, both inside and out. Comparing with the Newtonian potential U = γmg/r gives Uσ/U = r/σ, so "the only difference between the Newtonian and Relativistic Domain gravitational potentials is a relativistic one" — an expected consequence of D1 being a linear continuum.
Physical picture and consequences
The expansion enters the spatial dimensions at the source's centre with the velocity given by the constant term of viσ, is decelerated inside the body by an apparent "spatial re-absorption" represented by the variable term, and beyond the surface is attenuated only by the inverse-distance dependence. Bass notes the negative roots of vσ and viσ are equally valid solutions, describing a contraction of space and hence negative gravitation, whose importance he reserves for a promised cosmological paper. Because the expansion carries no energy it can exert no mechanical force: it "would simply flow past and through" other bodies. The only two effects on a nearby body are the negative acceleration from the Acceleration Potential and a smaller, velocity-dependent positive acceleration arising from motion through the varying temporal rate. One testable-sounding consequence is offered: since re-absorption occurs inside matter, the combined gravitational effect behind two aligned bodies "would be very slightly less than the sum of their individual gravitational potentials" — a shielding prediction. An appendix relates the D1 and D0 radial coordinates as σ = r(1 − vσ2/2c2)−1, and shows σi = 0 when ri = 0.
Assessment
What is genuinely attractive here is the ambition to supply a mechanism where the standard account supplies only geometry, and the honesty with which Bass labels the speculative parts. He does not claim experimental support; he says plainly that none exists and that he cannot see how to obtain it. The internal-solution derivation is careful about continuity: the boundary condition at σi = σg is imposed explicitly rather than assumed, the internal and external potentials match, and the recovery of Laplace and Poisson equations with an irrotational field is a real consistency check rather than decoration. The dimensional observation that γ(mass) has the units of a second time-derivative of volume is a neat piece of physical reading, and it is the one place in the paper where the expansion hypothesis looks motivated rather than merely permitted. That vσ = (2γm/σ)1/2 is the Newtonian escape velocity is also suggestive — the same quantity appears in the Gullstrand–Painlevé "river" form of the Schwarzschild metric, so Bass's picture of space flowing radially is not an idle analogy, and readers of that literature will find the result familiar.
The difficulties are serious. Most of the paper is not a derivation of the expansion hypothesis but a demonstration that it can be made consistent with results already established in [1]. The key step in Section 3.3.2 inserts the previously known Acceleration Potential d2σ/dτ2 = −γmg/σ2 into the volume equation, differentiates, and re-inserts the same relation to fix K0 = 12π. The answer vσ = (2γmg/σ)1/2 was already obtained trivially in Eq. (3.9) by equating (3.3) and (3.8); the longer route recovers it because it was fed in. K0 is thereby fitted, not predicted, and the "second-order rate of change of volume" premise does no independent work.
The elimination argument that establishes mechanism (iii) is weaker than the mathematics it supports. Only three possibilities are entertained, with no argument that the list is exhaustive; option (i) is discarded partly on a claim "stated here without proof" and deferred to an unwritten paper; and both rejections lean on the same objection — that the effect must also exist outside the source — which mechanism (iii) meets only by asserting that space itself flows, an assumption at least as strong as the ones being rejected. The energy argument is likewise assertive: the conclusion that the process consumes no energy rests in part on the author's inability to construct a derivation in which it does.
Against measurement, the paper's position is unclear because it defers the comparison to [1]. The claim that D1 reproduces General Relativity's gravitational characteristics is asserted, not shown here, and the results in this paper reproduce the Newtonian potential to first order with a relativistic correction of unspecified order. The paper never confronts the classical tests that discriminate at that order — the 43″/century anomalous perihelion advance of Mercury, the 1.75″ deflection of starlight at the solar limb (twice the Newtonian value), or the Shapiro delay — nor the Hulse–Taylor binary pulsar's orbital decay, which is a direct probe of a non-linear field theory with quadrupole radiation. A continuum that is "completely linear along all four axes" has no obvious mechanism for gravitational radiation at all, and the direct detection of Gravitational Waves a decade after publication makes that omission consequential. The internal solution's central value ui = (1 − 3α/σg)1/2 is, notably, the same limit as the interior Schwarzschild (Buchdahl) bound, but Bass flags it without exploring whether it agrees for the same reason.
Finally, the shielding prediction — a slight deficit behind two aligned bodies due to "re-absorption" — is the one place the theory offers something a measurement could settle, and it is exactly here that the paper offers no magnitude. Absorption-type gravity of this kind is tightly constrained by lunar and solar eclipse gravimetry and by the absence of anomalous heating in massive bodies (the classical objection to Le Sage-type Push Gravity); without a number the claim cannot be assessed. On its own terms the mathematics is competent and internally consistent, but the paper establishes compatibility rather than support, and Bass says as much in his concluding remarks, where the strongest evidence he claims is "circumstantial".