The Electrodynamic Origin of the Force of Gravity, Part 2
| Scientific Paper | |
|---|---|
| Title | The Electrodynamic Origin of the Force of Gravity, Part 2 |
| Read in full | Link to paper |
| Author(s) | Charles William Lucas |
| Keywords | Gravity, Electrodynamics |
| Published | 2009 |
| Journal | Foundations of Science |
| Volume | 12 |
| Number | 1 |
| No. of pages | 11 |
Read the full paper here
Abstract
The force of gravity is shown to be a small average residual force due to the fourth order terms in v/c of the derived universal electrodynamic contact force between vibrating neutral electric dipoles consisting of atomic electrons vibrating with respect to protons in the nucleus of atoms. The derived gravitational force has the expected radial term plus a new non-radial term. From the radial term the gravitational mass can be defined in terms of electrodynamic parameters. The non-radial term causes the orbits of the planets about the sun to spiral about a circular orbit giving the appearance of an elliptical orbit tilted with respect to the equatorial plane of the sun and the quantization of the orbits as roughly described by Bode's law. The vibrational mechanism that causes the gravitational force is shown to decay over time giving rise to numerous phenomena, including the expansion of the planets (including the earth) and moons in our solar system, the cosmic background radiation, Hubble's red shifts versus distance (due primarily to gravitational red shifting), Tifft's quantized red shifts (Bode's law on a universal scale), Tifft's measured rapid decay of the magnitude of red shifts over time, the Tulley-Fisher relationship for luminosity of spiral galaxies, the unexpected high velocities of the outer stars of spiral galaxies, and Roscoe's observed quantization of the luminosity and size (Bode's law) of 900 spiral galaxies. Arguments are given that this derived law of gravity is superior to Newton's Universal Law of Gravitation (F = Gm1m2 / r2) and Einstein's General Relativity Theory (Gμν = – 8πG/c2 Tμν).
Overview
This is the second instalment of Charles W. Lucas, Jr.'s programme, published through Common Sense Science, of deriving gravitation from electrodynamics rather than treating it as a separate fundamental interaction. Part 1 obtained the radial term; Part 2 does not add new derivation so much as look for what Lucas calls "corroborating circumstantial evidence" that the mechanism is real. Gravity, on his account, is not a field property of space but a statistical residue: the fourth-order-in v/c remainder of a universal electrodynamic contact force acting between neutral electric dipoles, each dipole being an atomic electron vibrating against the protons of its nucleus.
Two consequences carry the paper. First, oscillating dipoles must radiate, so all ordinary matter should be emitting; Lucas computes the wavelength of that emission for hydrogen and identifies it with the cosmic microwave background. Second, radiating means losing oscillation energy, so gravitational mass — being defined by the oscillation — must decay with time; Lucas takes the geological evidence usually read as plate tectonics and reads it instead as a growing Earth. Both consequences are stated as advantages over Newton and over Einstein's general relativity, which "explain less observed data". Much of what the abstract promises — Bode's law, Tifft's quantized redshifts, Tully-Fisher, flat rotation curves, Roscoe's 900 spiral galaxies — is announced here but not actually worked out in this instalment.
The argument
The radial term carried over from Part 1
The starting point is equation (18) of Part 1, which Lucas says has "the same form as Newton's Universal Law of Gravitation" F = −Gmg1mg2/r2, with the coefficient identified as
- Gmg1mg2 = (1/4πε0) (2/5π) e2 (A12ω12/c2)(A22ω22/c2)
where A is the amplitude and ω the angular frequency of the electron's vibration. Lucas is explicit that this is not a derivation of G: "there will be a range of combinations of amplitude A and frequency ω for which equation (18) above agrees with Newton's Universal Law of Gravitation." What the equation does is define gravitational mass in electrodynamic terms, mg ∝ A2ω2. He stresses three differences from Newton: the force is a local contact force, it decays over time by radiating, and it carries a second, non-radial term.
The wavelength of the dipole radiation
Taking hydrogen, which "comprises 75% of all visible matter", and setting A1 = A2 = A, ω1 = ω2 = ω, m1 = m2 = m, and substituting ω = 2πc/λ, the c4 cancels and equation (18) collapses to
- Gm2 = (1/4πε0)(2/5π) e2 16π4A4/λ4
so that
- λ4 = (2/5π) (e2/4πε0) 16π4A4 / Gm2
With G = 6.67390×10−11, 1/4πε0 = 9.0×109, e = 1.60217733×10−19 C, m = 1.6726×10−27 kg and A ≤ 0.37×10−10 m (the hydrogen atomic radius, since "the electron could not stay bound to the atom if it oscillated too far away from the nucleus"), Lucas obtains λ ≤ 146 mm — "in the microwave range". He then notes that the COBE spectrum peaks near 1 mm, far inside that bound, and concludes that the theory "can be made to simultaneously predict the measured experimental strength of the force of gravity and the observed cosmic background radiation by making the current amplitude of vibration of the electron equal to less than 1% of the radius of the atom", which he calls "a very reasonable value". He adds that a classical account of the blackbody distribution itself is available for finite-size toroidal electrons, without quantum mechanics.
Decay of gravity
Because the dipoles radiate, they lose oscillation energy, A2ω2 falls, and gravitational mass falls with it. Lucas argues the decay rate is position-dependent: atoms deep inside a body reabsorb radiation from their neighbours and lose energy slowly, atoms near the surface lose it fastest, so the rate scales with the volume-to-surface ratio. Large bodies therefore decay slowly — gravity inside the Sun weakens more slowly than inside a planet — and, extended to the cosmos, matter near the "centre of the universe" decays more slowly than matter near its edge, and the outskirts of a galaxy faster than its core.
Expansion as the test
The evidence Lucas offers is geological. He reads Marie Tharp's ocean-floor maps, the 1977 Office of Naval Research World Ocean Floor map and the 1997 Sandwell-Smith NOAA satellite map as "three dimensional stretch marks" recording an approximately 70% expansion of the Earth since its crust solidified, with the seam opening at the present Dead Sea, running down the Red Sea into the Indian Ocean and forking to form the Atlantic and Pacific. Hooke's law in three dimensions governs the slow stretching until the crust reaches its elastic limit and cracks. He cites current plate separation of about 25 cm per year, and argues that "only an expanding earth model can conserve energy and angular momentum for the movement of the continental plates". The magnetic striping of the sea floor is explained by polar wander driven by the expansion, and the closer spacing of older stripes is read as evidence that the expansion — hence the decay of gravity — was much faster in the past, "something like an exponential decay". Expansion cracks on Ganymede, the lunar maria and radar images of Venus are offered as the same process elsewhere.
Assessment
The programme has a real attraction: a single interaction instead of two, with gravitation emerging as a higher-order residue of electrodynamics between neutral bodies, is an old and respectable ambition, and Lucas is unusually forthright about what his equations do and do not do — he says plainly that (18) is a family of A, ω combinations consistent with G, not a computation of G.
The arithmetic checks. Evaluating λ4 = (2/5π)(16π4)(e2/4πε0)A4/Gm2 with his own constants gives λ4 = 4.60×10−4 m4, λ = 0.1465 m — 146 mm, exactly as printed. The expression is dimensionally sound (e2/4πε0 and Gm2 are both N·m2, so the ratio is the dimensionless electromagnetic-to-gravitational strength ratio, 1.24×1036 for protons). And since λ ∝ A, getting λ = 1 mm requires A = 1/146 of the atomic radius, i.e. 0.68% — so "less than 1%" is right too. There is no unit slip and no hidden power of ten here.
But the number is not a prediction. What the calculation actually shows is that λ/A ≈ 4×109, a fixed ratio set by the fourth root of the electromagnetic-to-gravitational strength ratio. A is a free parameter; nothing in the theory fixes it. Lucas's own wording concedes this — the theory "can be made to" predict the CMB "by making" A small enough. The only genuine content is the inequality A < atomic radius, which yields λ < 146 mm, and that bound is satisfied by every wavelength from 146 mm down to zero — by visible light, by X-rays, by anything. A test that cannot fail is not corroboration. This is a case where a fitted parameter is doing the work the mechanism is credited with.
Conflicts with measurement. Three are decisive and specific. (i) The theory says the radiation "should be greatest in the vicinity of matter". The CMB is isotropic to about one part in 105 once the kinematic dipole is removed, and it is emphatically not correlated with local matter; Lucas's Figure 2 skymap shows the dipole and the galactic plane, not a matter-tracing signal. (ii) The CMB is a blackbody. COBE-FIRAS showed deviations from a Planck spectrum below 5×10−5 of the peak — the most perfect blackbody ever measured. Dipole emission at a wavelength set by A and ω is line emission, and a superposition of atomic dipole lines is not a Planck curve; Lucas does not attempt to show it can be one. (iii) A "rapid decay" of gravitational mass is excluded directly. Lunar laser ranging constrains any secular change in the strength of gravity to |Ġ/G| below about 10−13 per year, with comparable bounds from binary pulsar timing and from Big Bang nucleosynthesis. Space geodesy (VLBI, SLR and GPS) puts the mean rate of change of the Earth's radius at 0.1 ± 0.2 mm per year — four orders of magnitude below what a 70% expansion over geological time requires. The 25 cm/yr Lucas quotes is the sea-floor spreading rate at ridges, which in conventional tectonics is balanced by consumption at trenches; treating it as radial growth is precisely the step that needs an argument, and the paper offers none beyond the assertion that "only an expanding earth model can conserve energy and angular momentum".
Steps asserted rather than derived. The volume-to-surface scaling of the decay rate is stated without calculation. So is the claim that the expansion causes polar wander and hence the magnetic striping — striping is explained conventionally by reversals of the geomagnetic field recorded in newly cooled basalt, and Lucas neither engages that account nor derives an alternative. Finally, defining mg ∝ A2ω2 for electron-proton dipoles leaves the theory owing an explanation of why gravitational mass tracks nucleon number so precisely across the periodic table, why neutrons — which carry no such dipole — gravitate at all, and why the equivalence principle holds to the 10−13 level in torsion-balance and lunar-ranging tests when the underlying A and ω would differ from element to element. The abstract's cosmological claims are not addressed in this instalment and cannot be assessed from it.