Gravitation, the "Dark Matter" Effect and the Fine Structure Constant
| Scientific Paper | |
|---|---|
| Title | Gravitation, the "Dark Matter" Effect and the Fine Structure Constant |
| Read in full | Link to paper |
| Author(s) | Reginald T Cahill |
| Keywords | Gravity, in-flow, fine structure constant, dark |
| Published | 2005 |
| Journal | Apeiron |
| Volume | 12 |
| Number | 2 |
| No. of pages | 34 |
| Pages | 144-177 |
Read the full paper here
Abstract
Gravitational anomalies such as the mine/borehole g anomaly, the near-flatness of the spiral galaxy rotationvelocity curves, currently interpreted as the "dark matter" effect, the absence of that effect in ordinary elliptical galaxies, and the ongoing problems in accurately determining Newton"s gravitational constant GN are explained by a generalisation of the Newtonian theory of gravity to a fluid-flow formalism with one new dimensionless constant. By analysing the borehole data this new constant is shown to be the fine structure constant 1/137. The spiral galaxy rotation curve effect and the globular cluster central "black hole" masses for M15 and G1 are then correctly predicted.
Overview
Reginald T Cahill of Flinders University argues in this 2005 Apeiron paper that a cluster of unrelated-looking gravitational anomalies — the mine and borehole g anomaly, the near-flat rotation curves of spiral galaxies, the absence of that flattening in ordinary elliptical galaxies, and sixty years of non-convergence in laboratory measurements of G — all follow from a single missing term in the theory of gravity. His diagnostic observation is that every decisive test of general relativity has been made in the regime of the external Schwarzschild metric, that is, outside a spherically symmetric mass, whereas each anomaly involves either a non-spherical matter distribution (spiral galaxies) or the interior of a spherical one (boreholes). The untested regime is exactly where the anomalies live.
The reformulation is to write gravity as a velocity field rather than an acceleration field. Cahill shows that the Schwarzschild metric can be transformed into Painlevé–Gullstrand form containing an explicit radial in-flow v(r) = −√(2GM/r)r̂, so that "in all cases the explicit tests of GR actually involved a velocity field." Newtonian gravity likewise rewrites exactly as a fluid in-flow, with g recovered as the Euler fluid acceleration ∂v/∂t + (v·∇)v. The two formalisms are mathematically equivalent — but only the velocity form admits a further generalization, and that generalization introduces one new dimensionless constant. Cahill's central claim is that fitting this constant to borehole gravity data yields α−1 = 139 ± 5, which he identifies with the fine structure constant 1/137.036. Dark matter, on this account, is not matter at all but the self-interaction of space, and quantum gravity effects are not confined to the Planck scale but are "relatively large and easily observed."
The argument
From metric to flow
Writing the proper time in the general form dτ2 = dt2 − (1/c2)(d'r(t) − v(r(t),t)dt)2, Cahill computes the geodesic equation explicitly and obtains a test-object acceleration in three parts: the Euler total fluid derivative ∂v/∂t + (v·∇)v; a Helmholtz term (∇ × v) × vR due to vorticity; and a relativistic term producing orbital precession and event horizons. That the result is independent of the test object's mass is the equivalence principle. He reads this decomposition as evidence "that the curved spacetime manifold mathematics was essentially concealing" a flow, and that the metric formalism "may have been misleading."
The new term and its constant
Since only the terms independent of the test-object velocity can belong to the flow dynamics itself, Newton's ∇·g = −4πGρ becomes ∇·(∂v/∂t + (v·∇)v) = −4πGρ. This admits a unique additional term:
- ∂(∇·v)/∂t + ∇·((v·∇)v) + C(v) = −4πGρ, C(v) = (α/8)((trD)2 − tr(D2))
with Dij the symmetrized velocity gradient. Crucially, C(v) vanishes for spherically symmetric flow, so the solar system — the source of Newton's law — is untouched, and Kepler's laws survive. Rewritten, the new term acts as an effective density ρDM = (α/32πG)((trD)2 − tr(D2)) appearing alongside real matter, and Cahill stresses that this "cannot be included, in a closed form, in the gravitational acceleration dynamics" — it exists only in the velocity formalism. With α = 0 the theory is exactly Newtonian.
To first order in α the effective density concentrates near the centre of a spherical system, and the total is MDM/M = α/2 independently of the density profile — a profile-free prediction he later uses on globular clusters. He notes in passing that this changes central g(r) enough that stellar structure theory would need revisiting, "which may have some bearing on the solar neutrino problem."
The borehole determination of α
For a body of radius R the theory gives an exterior inverse square law but with effective constant GN = (1 + α/2)G — so the measured Newtonian constant is not the fundamental one. Inside, the gravity residual Δg = gNewton − gobserved takes the form Δg(r) = −2παGNρ(R)(R − r) near the surface, linear in depth. Fitting the slope of the Greenland Ice Cap borehole data to 1.5 km, with measured ice density 930 kg/m3, gives α−1 = 139 ± 5. This is the paper's pivot: the constant is fitted here once and then used without further adjustment.
Spiral galaxies
In the matter-free asymptotic region the flow equation has an exact non-perturbative two-parameter solution
- v(r) = K[1/r + (1/RS)(RS/r)α/2]1/2
giving a circular orbital speed vO(r) = √(rg(r)) that falls off extremely slowly because of the small exponent α/2. Cahill compares this with the empirical Universal Rotation Curve of Persic, Salucci and Stel, fitted to some 1100 optical and radio rotation curves, and reports that his form with α = 1/137 and RS = 0.01Ropt essentially overlays the high-luminosity URC beyond x ≈ 1.5, and reproduces the non-Keplerian curve of NGC 3198.
The theory also has a separate one-parameter class of matter-free solutions v(r) = β/rα/4, which Cahill calls gravitational attractors. These, he suggests, were produced in the big bang, coalesce into larger ones, and seed spiral galaxies: large-β attractors capture more primordial gas and impart high angular momentum, producing spiral structure, while small ones yield galaxies without it. This is offered as the answer to why RS is small for spirals but effectively very large for the Earth and for elliptical galaxies — the latter being the case where planetary nebulae serving as test objects show Keplerian curves, an observation the dark matter hypothesis finds awkward.
Globular cluster "black holes"
The central attractors have an event horizon where the in-flow reaches c, but unlike general-relativistic black holes they contain no in-fallen matter. Numerical solutions confirm the perturbative MDM/M = α/2 = 0.00365. For M15, the reported central mass 1.7+2.7−1.7 × 103M☉ against a total 4.9 × 105M☉ gives 0.0035+0.011−0.0035; for G1, 2.0+1.4−0.8 × 104M☉ against (7–17) × 106M☉ gives 0.0006–0.0049. Both bracket α/2.
The scatter in measurements of G
Cahill then notes that the spread among sixty years of precision GN determinations is of relative size α/4, and attributes it to the differing mass geometries of Cavendish-type apparatus, each producing a different local "dark matter" polarization between the test masses. Taking the 1991 ocean Airy value GN = (6.677 ± 0.013) × 10−11 and removing the effect gives a fundamental G = (6.6526 ± 0.013) × 10−11, against the CODATA GN = 6.6742 × 10−11 which he regards as "contaminated." He concludes that Cavendish experiments are quantum gravity experiments and could be used to measure α in the laboratory.
What flows?
The final sections state the ontology. Cahill holds that the Michelson–Morley, Miller and DeWitte data do show a real absolute motion once gas-mode interferometers are analysed correctly — as a combination of geometric path difference, a physical Fitzgerald–Lorentz contraction, and the slowing of light in the gas, the first two cancelling exactly only in vacuum. On this reading the contraction is real rather than a perspective effect, and Miller's data yields both the Earth's orbital motion and an in-flow toward the Sun consistent with v = −√(2GM/r). But what flows is not matter through space: it is space itself, a quantum-foam system undergoing ongoing classicalisation, whose "flow" is a differential rearrangement of pattern connectivity with no absolute background. The Lense–Thirring effect becomes simple vorticity in this flow, and the in-flow equations' turbulence is claimed to be a new form of gravitational wave, unlike Einstein's.
Assessment
The paper's strongest feature is its structure as a prediction rather than a fit. Cahill fixes α once, from the Greenland borehole slope, and then applies the same number without adjustment to spiral rotation curves, to two globular clusters, and to the scatter in G measurements. The globular cluster test is the sharpest: MDM/M = α/2 is profile-independent at first order, so it is a genuine parameter-free number, and both M15 and G1 are consistent with it. The observation that all decisive tests of general relativity have sampled only the external Schwarzschild regime is correct and worth taking seriously, as is the observation that the Painlevé–Gullstrand form of that metric contains an explicit velocity field. The point about elliptical galaxies is also fair: a theory in which the effect is tied to flow geometry naturally distinguishes spirals from ellipticals, whereas a dark matter halo has to be given a reason not to appear.
The weaknesses, however, run deep. The identification of the new constant with the fine structure constant rests on one data set and a fit of 139 ± 5, which is compatible with 137.036 but equally compatible with a great many other numbers; the paper offers no derivation connecting a purely gravitational self-interaction coefficient to the electromagnetic coupling, only the suggestion that α may be "a generic measure of randomness." Without such a derivation the identification is numerology at the 1.5% level, and it is doing an enormous amount of interpretive work. The borehole anomaly itself is the weaker foundation of the two possible ones: Cahill notes in passing that "the reality of the effect was eventually doubted," and does not engage with why — the residuals are notoriously sensitive to the assumed density model of the overlying and surrounding material, and the standard resolution attributes them to terrain and density inhomogeneity rather than new physics.
On galaxies, the fit to the Universal Rotation Curve is presented as agreement, but RS is a free parameter adjusted per galaxy and acknowledged to depend on luminosity, so the "prediction" for rotation curves is a one-parameter family fitted to a one-parameter empirical family — considerably weaker than the globular cluster test. More seriously, the theory as presented is a modification of the non-relativistic flow dynamics, and the strongest modern evidence for dark matter is not rotation curves at all but observations the paper does not address: the acoustic peak structure of the CMB power spectrum, which requires a non-baryonic gravitating component that does not couple to photons; the offset between the lensing mass and the baryonic gas in the Bullet Cluster; and the growth of large-scale structure. A modification that adds an effective density rigidly tied to the local matter flow cannot easily reproduce a mass distribution spatially separated from its baryons.
The G argument is presented as explanation but is the least constrained claim in the paper: noting that a scatter is "of order α/4" is a statement about magnitude only, and the actual mechanism — polarization of the central dark matter effect between two Cavendish masses — is asserted without calculation for any specific apparatus. A genuine test would be to compute the predicted shift for two experiments of known differing geometry and show it accounts for their difference; Cahill proposes this as future work rather than doing it. Meanwhile the G scatter has since narrowed considerably as systematics have been understood, which is what one expects of measurement error rather than of a real geometry-dependent effect.
Finally, the absolute-motion section imports a large and separately contested body of claims — that Michelson–Morley and Miller detected a real aether drift — on which the gravitational argument does not actually depend. This is a strategic weakness: the in-flow formalism and the C(v) term stand or fall on the borehole, galaxy and cluster data, and attaching them to the interferometer reanalysis gives a critic an easy route to dismissing the whole. On its own terms the paper is internally consistent and admirably specific about what would test it — laboratory extraction of α from Cavendish geometry is a real, falsifiable proposal — but the central identification of the new gravitational constant with α remains, on the evidence given here, a suggestive coincidence rather than a demonstrated result.