View source for A Coherent Dual Vector Field Theory for Gravitation

{{Infobox paper
| title = A Coherent Dual Vector Field Theory for Gravitation
| url = [http://www.naturalphilosophy.org/pdf/abstracts/abstracts_4894.pdf Link to paper]
| author = [[Thierry De Mees]]
| keywords = [[gravity]], [[star: rotary]], [[disc galaxies]], [[gravity repulsion]], [[relativity]], [[gyrotation]], [[gravitomagnetism]], [[chaos]], [[Heaviside field]], [[Lorentz force]], [[angular momentum]], [[binary star]]
| published = 2003
| journal = [[General Science Journal]]
| num_pages = 14
}}

'''Read the full paper''' [http://www.naturalphilosophy.org/pdf/abstracts/abstracts_4894.pdf here]

==Abstract==

This publication concerns the fundamentals of the dynamics of masses interacting by gravitation. We start with the Maxwell Analogy for Gravitation (or the "Heaviside field"), and we develop a model. This model of dynamics, allow us to quantify the transfer of angular movement point by point by the means of vectors, and to bring a simple, precise and detailed explanation to a large number of cosmic phenomena. And to all appearances, the theory completes gravitation into a wave theory. With this model the flatness of our solar system and our Milky way can be explained as being caused by an angular collapse of the original orbits, creating so a density increase of the disc. Also the halo is explained. The "missing mass" (dark matter) problem is solved, and without harming the Keplerian motion law. The theory also explains the deviation of mass like in the double-lobed shape of rotary supernova having mass losses, and it defines the angle of mass losses at 0° and under 35°16'. Some quantitative calculations describe in detail the relativistic attraction forces maintaining entire the fast rotating stars, the tendency of distortion toward a toroid-like shape, and the description of the attraction fields outside of a rotary black hole. Qualitative considerations on the binary pulsars show the process of cannibalization, with the repulsion of the mass at the poles and to the equator, and this could also explain the origin of the spin-up and the spin-down process. The bursts of collapsing rotary stars are explained as well. The conditions for the repulsion of masses are also explained, caused by important velocity differences between masses. Orbit chaos is better explained as well. Finally, the demonstration is made that gyrotation is related to the Relativity Theory.

==Overview==

This is the founding paper of De Mees' "gyro-gravitation" programme, developed from the [[Oliver Heaviside|Heaviside]] analogy between [[Maxwell's Equations|Maxwell's equations]] and [[Gravity|gravitation]]. Its premise is that gravitation is not a single scalar-sourced field but a dual vector field: alongside the ordinary acceleration field ''g'' there is a second, circulation-type field the author names ''gyrotation'' (symbol '''Ω''', dimensions rad/s), generated by mass in motion exactly as the magnetic field is generated by moving charge. The paper's programme is to write out the full Maxwell-analogue set, then apply it to a long list of astrophysical phenomena without introducing any new entity beyond ordinary matter.

The departure from the mainstream account is that all of this is done in flat Euclidean space with universal time. De Mees does not curve spacetime; he adds a velocity-dependent term arising from the finite propagation speed of gravitational influence, and argues in his final section that this term ''is'' what general relativity models geometrically. The most consequential claim is that flat galactic rotation curves follow from the geometry of an angularly collapsed disc, so that [[Dark Matter|dark matter]] is unnecessary — "the velocity constancy is entirely due to the formation of the plane galaxy without a need of invisible masses."

==The argument==

===The field equations===

De Mees substitutes mass for charge, gyrotation for magnetic field, and writes ''G''<sup>-1</sup> = 4''πζ''. The set is:

: '''F''' ⇐ ''m''('''g''' + '''v''' × '''Ω''')
: ∇ · '''g''' ⇐ ''ρ''/''ζ''
: ''c''<sup>2</sup> ∇ × '''Ω''' ⇐ '''j'''/''ζ'' + ∂'''g'''/∂''t''
: ∇ · '''Ω''' = 0
: ∇ × '''g''' ⇐ −∂'''Ω'''/∂''t''

with ''c''<sup>2</sup> = 1/(''ζτ'') and ''τ'' = 4''πG''/''c''<sup>2</sup>. A notational point he emphasises: the sign ⇐ replaces = wherever "the right hand of the equation induces the left hand", to keep the causal direction explicit. The ∂'''g'''/∂''t'' term is added for Maxwell's own reason, compliance with mass continuity, div '''j''' ⇐ −∂''ρ''/∂''t''. In integral form the third equation becomes ∮'''Ω'''·d'''l''' ⇐ 4''πGm''/''c''<sup>2</sup>, which he calls the law of gravitational motion transfer. He credits Heaviside (1893), Nielsen (1972), Negut (1990), Jefimenko (2000) and Tajmar and de Matos (2003) with independent versions of the analogy.

The physical picture he attaches is that a small moving gravitational field polarises the large symmetric one, producing "a force field which is perpendicular to the gravitation force field, but which annihilates itself if no polarisation has been induced".

For a rotating sphere he integrates the dipole contributions as one would for a magnetic dipole, obtaining interior and exterior gyrotation fields; the exterior result for a homogeneous rigid sphere is

: '''Ω'''<sub>ext</sub> ⇐ −(''G''/5''c''<sup>2</sup>) (''mR''<sup>2</sup>/''r''<sup>3</sup>) ['''ω''' − 3('''ω'''·'''r''')'''r'''/''r''<sup>2</sup>]

===Angular collapse and disc formation===

The first application is the flatness of the solar system and of spiral galaxies. An orbiting mass ''m''<sub>p</sub> in the gyrotation field of a spinning centre acquires '''a'''<sub>p</sub> ⇐ '''v'''<sub>p</sub> × '''Ω'''<sub>p</sub>. The tangential component always drives the orbit toward the central body's equatorial plane; a retrograde orbit has the sign of the tangential acceleration reversed, so its plane is turned until the orbit becomes prograde. The result is a damped oscillation about the equator — a precession with decreasing amplitude — and hence an angular collapse of the orbit population into a prograde disc. The radial component produces a slow shrinkage or growth of the orbit depending on the sign of ''ω''<sub>p</sub>. A spinning secondary additionally acquires a precession from the momentum ''M''<sub>Z</sub> ⇐ 2''ω''<sub>Y</sub>''X''<sup>2</sup>''Ω''<sub>p</sub> cos ''δ''.

Objects with no initial orbital motion behave differently: they oscillate widely about the galaxy's rotation axis, deviated retrograde while falling in and prograde while receding, and De Mees notes that here "the analytical description of the evolution is not successful any more" and only numerical work will do. He suggests globular clusters follow this non-orbital pattern rather than converging on the galactic centre.

===Rotation curves without dark matter===

The disc-formation result is then used against dark matter. Before collapse the mass occupies (4/3)''πR''<sup>3</sup>; afterwards it is compressed into ''πR''<sup>2</sup>''h'' with ''h'' a small fraction of the original diameter, so a star at radius ''R'' feels more gravitation than the bulge alone would supply. Taking the enclosed mass to grow as ''n''·''M''<sub>o</sub> at radius ''k''·''R''<sub>o</sub> with ''k'' and ''n'' linear in distance, the orbital relation becomes ''v''<sub>r</sub><sup>2</sup> = ''GnM''<sub>o</sub>/''kR''<sub>o</sub>, which is constant in ''R''. Applied to the Milky Way with a bulge of 10,000 light years' diameter and 20 billion solar masses (10% of the galaxy), and setting ''k'' = ''n'', he obtains an orbital velocity of 240 km/s against an observed curve near 250 km/s.

===Compact stars, mass loss and the 35°16' angle===

For a fast-rotating sphere the gyrotation force at the surface points inward, adding a compression term to gravity and centrifugal repulsion. Setting the bracketed factor to zero gives a Critical Compression Radius ''R''<sub>Cα</sub> < ''R''<sub>C</sub>(1 − 3 sin<sup>2</sup>''α''), with the equatorial value

: ''R''<sub>C</sub> = ''Gm''/5''c''<sup>2</sup>

which he notes is one tenth of the Schwarzschild radius, and from which he draws two striking conclusions: "black holes can explode when they are fast spinning", and "every non-exploding spinning star must be a black hole". The vanishing of the bracket at sin<sup>2</sup>''α'' = 1/3 gives ''α'' = 35°16', beyond which the critical radius is zero and the star's shape stretches toward a Dyson ellipse and then a toroid — he cites Ansorg, Kleinwächter and Meinel (2003) as numerical support.

The same angle then explains the geometry of [[Supernova|supernova]] mass loss. Near the poles, between 35°16' and 144°44', the gyrotation points perpendicular to the surface so the gyrotation acceleration is tangential and cannot balance the centripetal force; at the equator there is no gyrotation force either. Mass therefore escapes at 0° and near 35°16', producing the symmetric lobes with a central disc seen in SN 1987A and η Carinae. De Mees offers this as a prediction: "observation will have to verify that these lobes start nearly at 35°, measured from the equator."

===Solar dynamo, accretion discs and repulsion===

Resolving the same forces into tangential and radial components at the solar surface gives a flow of surface mass toward the equator and an inward push that increases toward the equator, which he offers as the mechanism behind the roughly 11-year migration of sunspots and two toroidal internal circulations. He concedes the differential rotation of the Sun is not explained.

For a binary with an accretion disc, prograde ring material is drawn radially in, deviated retrograde as it approaches, then projected away from the poles by a further '''v''' × '''Ω''' deviation, while equatorial material is returned to the disc — a cycle he offers as the origin of spin-up and spin-down and of polar beams. A collapsing rotating star, by ∇ × '''g''' ⇐ −∂'''Ω'''/∂''t'', generates a circular rather than radial gravitational force in the accretion ring, contracting it and expelling matter as a burst at the poles and at the ring. Repulsion is a general consequence: parallel mass flows attract, antiparallel ones repel. He also notes that the X-rays accompanying bursts are unlikely to be gravitational waves, and speculates that particles driven through the ether faster than light might be destabilised so that "trapped light" escapes as X-rays.

Applied to two planets in near passage, gravitational attraction pulls the smaller into a tighter orbit while gyrotation slows its orbital velocity, contradicting the Keplerian speed–radius relation; the conflict is resolved by the planet being sent outward, contradicting it again, and the alternation sustains an oscillation. Gravitation alone, he argues, would damp the oscillation; gyrotation maintains it.

===The relativity connection===

The final derivation compares two parallel mass flows as seen by a resting and a co-moving observer. The resting observer attributes work to gravitation plus gyrotation, giving the term 2''Gm''<sup>2</sup>''v''<sup>2</sup>/(''rc''<sup>2</sup>)d''r'' alongside 2''Gm''<sup>2</sup>/''r'' d''r''; the co-moving observer attributes it to gravitation alone. Equating the two and applying the relativity principle yields (''m''<sub>st</sub>)<sub>st</sub> = (''m''<sub>v</sub>)<sub>st</sub>√(1 − ''v''<sup>2</sup>/''c''<sup>2</sup>). De Mees concludes that "the 'relativistic effect' of gravitation, or better, the time delay of light, is expressed by gyrotation", and that relativistic mass increase is "an equivalent pseudo mass due to the gyrotation forces which act locally on every point" — so that with both fields included, the frame may be chosen freely while still obtaining a relativistic result.

==Assessment==

The attractive features are real. The Maxwell analogy for gravitation is not fringe: the linearised weak-field limit of general relativity does contain a gravitomagnetic sector with equations of essentially this shape, and the [[Gravitomagnetism|gravitomagnetic]] field has since been measured directly by Gravity Probe B's frame-dragging result. De Mees is therefore working with a structure that has independent standing, and his exposition of it is unusually clear and physically motivated. The programme's ambition — one field theory, Euclidean, with no dark matter, no curved spacetime and no free parameters, applied to a dozen distinct phenomena — is coherent in intent, and some of its qualitative outputs (prograde disc formation from an initially isotropic distribution, the double-lobed geometry of rotary supernova ejecta) are the right ''kind'' of consequence to draw from a velocity-dependent force. The 35°16' angle is a genuine prediction with an observable signature, and stating it as one is to the paper's credit.

The central difficulty is one of magnitude, and the paper never confronts it. Gravitomagnetic effects carry a factor of ''v''<sup>2</sup>/''c''<sup>2</sup>, which for galactic rotation (''v'' ≈ 250 km/s) is of order 10<sup>-6</sup>. The flat-rotation-curve derivation in section 6 does not in fact use gyrotation at all: it uses gyrotation only to argue that a disc forms, and then obtains ''v''<sup>2</sup> = constant from an assumed linear enclosed-mass profile ''n''·''M''<sub>o</sub> at radius ''k''·''R''<sub>o</sub> with ''k'' = ''n'' — that is, ''M''(''R'') ∝ ''R'', which is precisely the mass distribution that ''defines'' a flat curve in ordinary Newtonian gravity. The assumption is the conclusion. Nothing in the paper shows that disc compression of the visible mass yields that profile at the radii where curves stay flat, and observationally it does not: the flatness persists far beyond the optical disc, where there is little luminous matter to compress. That the Milky Way number comes out at 240 km/s is unsurprising when the bulge mass and the linearity constant are both chosen inputs.

Several other steps are asserted rather than derived. The Critical Compression Radius follows from setting one bracket to zero, but the inference from it that "every non-exploding spinning star must be a black hole" is a statement about all stars drawn from a formula developed for a homogeneous sphere at extreme spin, and no rotating main-sequence star is checked against it. The 35°16' angle derives from the same bracket and is therefore only as good as the rigid homogeneous-sphere model; real supernova progenitors are strongly differentially rotating and centrally condensed. The X-ray speculation involving particles moving "probably faster than light" through the ether is offered without any supporting calculation and sits uneasily beside the paper's own use of ''c'' as the propagation speed. And the closing relativity derivation obtains the Lorentz factor from a one-dimensional work comparison between two idealised mass flows; that this recovers √(1 − ''v''<sup>2</sup>/''c''<sup>2</sup>) in one configuration does not establish the general claim that gyrotation "expresses" relativistic effects.

Against established measurement, the theory owes accounts it does not give. General relativity's classical tests are quantitative — the 43 arcseconds per century anomalous perihelion advance of Mercury, the Shapiro delay, and the orbital decay of the binary pulsar PSR B1913+16, which matches the quadrupole gravitational-wave prediction to better than a percent. A Euclidean vector theory of this type generically gets the light-bending and perihelion coefficients wrong by factors of order unity, and radiates dipole as well as quadrupole waves, which the binary pulsar excludes. None of these are addressed. Finally, several sections — the solar dynamo, the accretion-disc cycle, orbital chaos — are qualitative narratives illustrated by figures rather than calculations, and are labelled as such by the author, which is honest but limits how much weight the "coherent" of the title can carry.

==See also==
* [[Thierry De Mees]]
* [[Gravitomagnetism]]
* [[Oliver Heaviside]]
* [[Maxwell's Equations]]
* [[Dark Matter]]
* [[Black Hole]]
* [[Supernova]]
* [[Toroidal Ring]]
* [[Gravitational Waves]]
* [[Relativity]]

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