Electrodynamic Origin of Gravitational Forces

Scientific Paper
Title	Electrodynamic Origin of Gravitational Forces
Read in full	Link to paper
Author(s)	Charles William Lucas
Keywords	electrodynamics, gravity, Bode's Law, red shifts, gravity decay, MOND, red shift decay
Published	2011
Journal	Proceedings of the NPA
Volume	8
No. of pages	12
Pages	375-386

Read the full paper here

Abstract

From the derived universal classical electrodynamic contact force law for finite-size elastic particles the force of gravity is identified as a statistical residual force of the fourth order term in v/c due to the vibration of neutral electric dipoles consisting primarily of atomic electrons and nuclear protons plus polarized vibrating neutrons in the nucleus. The gravitational force is calculated and found to be a relativistic version of the customary radial term of Newton's Universal Law of Gravitation plus a new non-radial term. From the radial term the gravitational mass is defined in terms of electrodynamic parameters. The non-radial term gives rise to an (R^.V)R x (R x V) force that 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 with periods in agreement with Bode's Law. The vibrational mechanism causing the gravitational force decays over time giving rise to the cosmic background radiation plus Hubble's Law for red shifts versus distance due to gravitational red shifting. Halton Arp's discovery of quasars bound to galaxies with significantly different red shifts is explained in terms of the younger quasar galaxy's neutral electric dipole vibrations having decayed for a shorter period of time than those of the older and larger associated galaxy. The decay of gravity also explains Tifft's measured decay of the magnitude of red shifts over time and the high velocity of stars in the spiral arms of galaxies.

Overview

Charles W. Lucas, Jr., writing for Common Sense Science and presented at the 2011 NPA meeting in College Park, argues that gravity is not a fundamental interaction at all but a small statistical leftover of electrodynamics. The paper applies his previously derived "universal classical electrodynamic contact force law" for finite-size elastic charged particles to a pair of neutral, oscillating electric dipoles — in practice, atomic electrons vibrating against nuclear protons — expands the force in powers of β = v/c, and identifies the surviving fourth-order term as the force of gravity.

The departure from the mainstream is total, and Lucas says so: "mass is not a fundamental quantity of nature," and the notions of mass intrinsic to Newton's law and to Einstein's general relativity "appear to be false." Gravity in this account is a local contact force mediated by extended fields rather than an action-at-a-distance or a curvature of space-time; it is attractive only; and, crucially, it decays with time, because the dipole oscillations that generate it radiate their energy away. That single consequence is then used to sweep up a long list of disputed observations — the cosmic microwave background, the expansion of the Earth, Hubble's redshift-distance law, Halton Arp's discordant quasars, Tifft's quantized redshifts, flat galactic rotation curves — all without dark matter or dark energy, which Lucas calls "illogical and unphysical."

The framing is that of the electric universe school. Lucas opens with images of the Eskimo and Cat's Eye nebulae to argue that space is not empty but filled with structured plasma, that intergalactic magnetic filaments connect matter across millions of light years, and that the electrodynamic force is 10⁴⁰ times stronger than gravity and should therefore dominate cosmic organisation. He also invokes Poincaré's argument that two forces sharing the same mathematical form and the same fundamental constants cannot both be fundamental — general relativity being expressed through c, the constant of electrodynamics.

The argument

The order-of-magnitude motivation

Lucas's opening estimate is the most immediately checkable thing in the paper, and it holds up. Combining the Lorentz force law with Ampère's law for a moving charge adds to the static Coulomb field a term of order v²/c². Taking a typical free-electron drift velocity in a conductor of about 0.03 m/s, that ratio is about 10^-20, so the next order, v⁴/c⁴, is about 10^-40. Gravity is roughly 10^-40 times weaker than the static Coulomb force between the same particles — the electron-proton ratio is about 2×10³⁹. The coincidence is real, and it is the whole reason for looking at the β⁴ term. Lucas notes that such higher-order terms "were never fully investigated" in the past.

The averaging

The universal force law is expanded binomially in β, keeping terms to fourth order, and yields two structurally different pieces: a radial term along R, and a non-radial term proportional to (β·R){R×(R×β)}. Lucas then computes the force between two neutral dipoles, each a proton-electron pair, summing the four charge-pair forces (++, +−, −+, −−). Because the proton is 1836 times heavier, the vibration is treated as the electron's alone. The dipole separations A₁, A₂ are dropped from the denominators, which is legitimate for laboratory distances where r ≫ A.

Three averages are then performed: over the phase φ of each oscillator, over the relative orientation θ, and over time. The phase averages kill all odd powers of sine, and the first-order (unity) terms of the four pair forces cancel identically — which is simply the statement that two static neutral atoms exert no net force. What survives is the cross term at fourth order. The angular integral over θ of (−1/8 − cos²θ/4 + 3cos⁴θ/8) contributes a factor of 4/π, giving an attractive-only residual force of the Newtonian 1/R² form, with the gravitational mass now defined in terms of electrodynamic parameters — charge, oscillation amplitude A, and angular frequency ω.

(Note for readers: the equations in the archived PDF do not survive text extraction — operators, subscripts and Greek letters are dropped or replaced. The structure above is reconstructed from the surrounding prose and the paper's own verbal descriptions rather than transcribed.)

The microwave prediction

Setting the derived expression equal to Gm₁m₂/R² for hydrogen fixes a relation between A and ω. Because the force goes as A⁴ω⁴ and ω = 2πc/λ, the wavelength scales linearly with the amplitude. Lucas evaluates the upper bound — the electron cannot oscillate further than the atom's own radius — and obtains λ ≤ 146 mm, which he notes is in the microwave range. He then observes that the measured cosmic background radiation peaks near 1 mm, and remarks that both the strength of gravity and the observed background can be predicted at once "by making the current amplitude of vibration of the electron equal to less than 1% of the radius of the atom." That step is internally consistent: λ ∝ A, so 1% of 146 mm is about 1.5 mm.

Decay of gravity and an expanding Earth

Because the oscillators radiate, they must run down, so gravity weakens with time. The rate depends on volume-to-surface ratio, so atoms deep inside a large body lose energy more slowly than those near its surface, and large bodies decay more slowly than small ones. Lucas takes the evidence for decay to be an expanding Earth: the Tharp ocean-floor maps, the ONR World Ocean Floor map of 1977 and the Sandwell-Smith satellite map are read as "three-dimensional stretch marks" recording roughly 70% expansion since the crust solidified, with a current rate of about 25 cm per year, beginning at the Dead Sea and running down the Red Sea before forking into the Atlantic and Pacific. The magnetic striping parallel to the mid-ocean ridges is attributed to polar wander driven by that expansion, and the wider spacing of older stripes to an early phase of much faster gravitational decay. Expansion cracks on Ganymede, the lunar maria and radar features on Venus are offered as parallels.

Spiral orbits, Bode's Law and quantization

The non-radial (R·V)R×(R×V) term is suppressed by β² relative to the radial term and adds a corkscrew to what would otherwise be a circular orbit in the sun's equatorial plane. Lucas argues that a spiralling orbit is stable only if it returns to the same point, which quantizes the orbits, and that the observed tilt of the planetary orbits with respect to the sun's equatorial plane — and the appearance of ellipticity — is the projection of such a spiral. He points to Bode's Law for the planets and for the moons of Uranus, and reads Roscoe's finding of discrete sizes and luminosities among 900 spiral galaxies as the same law reappearing on a cosmic scale.

Redshift

The redshift argument runs through the gravitational redshift z = Δλ/λ = GM/Rc², confirmed by Pound and Rebka in 1960. If gravity was stronger in the past, light emitted long ago left a deeper potential well and is more redshifted — giving Hubble's law without expansion, with the Doppler contribution a small scatter about the main trend. Arp's case of Markarian 205 (z = 0.07) apparently connected to NGC 4319 (z = 0.0056) becomes a young, less-decayed object beside an older one. Tifft's periodicity of Δz ≈ 0.00024, with submultiples at 1/2, 1/3, 1/4 and 1/8 seen most sharply in the frame at rest with the microwave background, is read as Bode's Law on the largest scale, implying that the universe has a geometric centre. Tifft's reported secular decrease of galactic redshifts over a few years is taken as direct confirmation of decaying gravity. Finally, flat rotation curves and the Tully-Fisher relation are explained by mass loss: the outer stars of a galaxy decay faster than the core, so they are now in the process of escaping a centre that can no longer hold them.

Assessment

The paper's genuine attraction is that it is a mechanism, not a fit. It starts from one force law, identifies a specific physical process (dipole oscillation), and derives an inverse-square attractive-only force with the right sign and, given a free parameter, the right magnitude. The v⁴/c⁴ motivation is a real numerical coincidence that anyone can check in a line, and the cancellation of the leading terms between the four charge pairs is exactly what one should demand. It also makes falsifiable predictions rather than retrodictions, and it is admirably explicit that all of them "must be observed in order to claim that this force law is valid." Lucas is right, too, that a theory in which gravity is not a force sits awkwardly with the equality of inertial and gravitational mass, which general relativity assumes rather than explains.

Against that, several difficulties are severe, and some are arithmetic.

The gravitational redshift cannot reach the required size. This is the sharpest failure, and it uses only the paper's own equation (30). For the sun, GM/Rc² = 2.1×10^-6. To produce Markarian 205's z = 0.07 by this mechanism requires GM/R about 33,000 times the solar value; to produce z ≈ 1, as observed for ordinary distant galaxies, requires about 470,000 times. Since M and R are those of ordinary stars, the whole factor would have to come from a formerly enormous G. A G five to six orders of magnitude larger in the relatively recent past is incompatible with stellar structure, with the Earth's own liquid-water history, and with the paper's own picture of slow secular decay. Lucas does say the model spans "at least 9 orders of magnitude change in the observed red shifts," but the paper never carries out this check.

Redshift would depend on the emitting star, and it does not. A gravitational-redshift interpretation predicts that z varies with each source's M/R. Within a single galaxy, giants and main-sequence dwarfs differ in M/R by orders of magnitude, yet their measured redshifts agree. The effect itself is real and measured — white dwarfs in the Hyades show gravitational redshifts of tens of km/s, distinguishable from their cluster's motion — which is precisely why its absence at the galactic level is decisive.

Callisto's period. Lucas reads Fig. 17 as showing spiral periods for Jupiter's moons in the ratio Io = 2, Europa = 4, Ganymede = 8, Callisto = 16. The first three are the Laplace resonance and are correct: 1.769 d, 3.551 d and 7.155 d give ratios of 1 : 2.007 : 4.044. Callisto's period is 16.689 d, which is 9.43 times Io's, not 16. Callisto is famously not in the Laplace resonance, and the doubling sequence the argument depends on breaks at the fourth moon.

An internal slip on the wave equation. Introducing the dipole oscillations, the paper writes "from the wave equation Af = c" and infers frequencies "in the microwave range ≈ 10¹⁰ per second" from an amplitude A ≈ 10^-10 m. But c/10^-10 m is 3×10¹⁸ Hz; the microwave figure comes from λf = c with λ ≈ 3 cm. The later derivation uses λf = c correctly, so this is a slip rather than a load-bearing error, but it conflates the amplitude with the wavelength at exactly the point where the reader is being asked to accept that the two are related.

The microwave background is the wrong kind of radiation. COBE's FIRAS instrument found the CMB spectrum to be a blackbody to better than about 50 parts per million — the closest blackbody ever measured. Radiation from bound atomic dipole oscillators of a characteristic amplitude and frequency would not be thermal, and matching a peak wavelength is not the same as matching a spectrum. Lucas's Fig. 5 is captioned as showing "variations reflecting the matter distribution in space"; the dominant band across the COBE two-year skymap is Milky Way foreground emission, and once the dipole and the Galaxy are removed the residual anisotropy is about one part in 10⁵ and does not trace nearby matter. A background generated by local matter should be brightest toward matter, and it is not.

The decay rate is bounded by measurement. Lunar laser ranging and planetary ephemerides constrain any secular change in the gravitational constant to |Ġ/G| below roughly 10^-13 per year. Satellite geodesy limits any change in the Earth's mean radius to well under a millimetre per year, against the paper's 25 cm per year. Seafloor spreading is real and is measured at the rates Lucas cites, but the plate-motion budget closes because spreading is matched by subduction — a process the paper does not address. And a classical ground-state atom whose electrons continuously radiate is the exact difficulty that classical atomic physics could not survive; Lucas's own toroidal ring programme with David L Bergman is elsewhere designed to give non-radiating stable orbits, which sits uneasily with a gravity that exists only because those same electrons radiate.

Finally, the paper's structure is cumulative rather than probative: each anomaly is shown to be consistent with decaying gravity, and no observation is identified that would count against it. The Arp connection is attributed here to "gamma ray spectroscopy," where the original claim rested on optical imaging of a disputed luminous bridge, and NGC 4319 is once misnumbered 4316. These are small, but in a paper that asks the reader to discard both Newton and Einstein on the strength of an accumulated case, the case has to be audited item by item, and several items do not survive the audit.

See also

• Charles William Lucas
• Common Sense Science
• David L Bergman
• Toroidal Ring
• Halton Arp
• William G Tifft
• Anthony L Peratt
• Wallace Thornhill
• Eric J Lerner
• Redshift
• Dark Matter
• Dark Energy
• Cosmic Microwave Background
• Electrodynamics
• Coulomb's Law