An Electrostatic Solution for the Gravity Force and the Value of G
| Scientific Paper | |
|---|---|
| Title | An Electrostatic Solution for the Gravity Force and the Value of G |
| Read in full | Link to paper |
| Author(s) | Morton F Spears |
| Keywords | gravity, force, forces |
| Published | 2010 |
| Journal | Galilean Electrodynamics |
| Volume | 21 |
| Number | 2 |
| No. of pages | 10 |
| Pages | 23-32 |
Read the full paper here
Abstract
Written in 1999, published posthumously. This paper claims that gravity is electrostatic, and substantiates this claim by deriving, through basic electrostatic relationships, a simple equation for gravity forces that includes an expression for the gravity constant G in terms of electrostatic parameters. Applied to interaction between two separated sub-atomic particles in open space, the derivation of G results in a value that falls within the range of the currently best known and accepted empirical measurements. The general electrostatic gravity equation next derived is applicable for all physical entities, however small, or large, thus presenting a comprehensive new way of perceiving and understanding gravity forces. A variety of other important conclusions also follow. For example, the electrostatic approach helps to explain why, regardless of the precision of their measurements, experimenters who use different physical layouts may continue to find different empirical values for G.
Overview
Spears was an electronics engineer who spent the last two decades of his life on a "Capacitance Theory of Gravity", set out in two self-published books (1991 and 1993) and condensed into this paper, communicated posthumously to Galilean Electrodynamics by his daughter Leigh Spears Tesfatsion. The thesis is that gravity is not a separate interaction at all but a residual electrostatic effect, and the paper's headline result is a value for G computed from purely electrical quantities: charge, permittivity, the electron mass, the proton-to-electron mass ratio and the speed of light.
The mechanism proposed is a second kind of field. Alongside the familiar volts-per-metre gradient V/r, Spears posits a volts-per-daraf gradient V/S, where the daraf is the reciprocal farad — the unit of elastance. He argues that in a neutral pair of hydrogen atoms the ordinary Coulomb V/r fields cancel exactly, leaving only this residual V/S "field", which is so weak that it moves no charges, cannot be polarised away and cannot be screened by any Faraday cage — and which, when converted into ordinary units, yields forces of exactly gravitational magnitude. The departure from the mainstream is therefore not a modification of gravity but an elimination of it: there is no separate gravitational interaction and no independent constant G, only a calculable consequence of electrostatics.
The argument
The two-hydrogen model
The model of Figure 1 is two hydrogen atoms one metre apart in free space, at rest relative to one another. Electron 1 and proton 3 lie in the first atom; electron 2 in the second. The capacitances are those of small conducting spheres: C1 = 4πε0Re to the background; C12 = 4πε0Re2/r between the two electrons; C32 = 4πε0PRe2/r from proton to distant electron; and C123 their series combination. Thévenin's theorem then gives the voltage induced at electron 1 by the distant proton,
- V1x = Qp / [(P + 1) 4πε0r]
with P = Mp/Me = 1836.15. The electron's effective radius is the classical electron radius Re = Qe2/4πε0Mec2 = 2.81795 × 10−15 m, obtained by equating Qe2/Ce to Mec2.
The conversion factor K
The heart of the paper is a change of the distance appearing in the force law. The ordinary electrostatic force between capacitor poles is F = QV/2r. Spears counts the elastance of C12 as S12 = r/4πε0Re2 = 1.13181 × 1039 darafs, defines D as the number of metres and N as the number of darafs, and forms
- K = D/N = 4πε0Re2 farad-metres / 1 farad-metre = 8.83538 × 10−40
which he declares to be "a pure number". A quantity r* is then defined by r*K = r, and the gravitational force is taken to be the same expression with r* in place of r:
- Fge = QV/2r* = (1/2)KQV/r = KF
With Q = Qe and V = V1x and r = 1 m this gives Fge = −5.54779 × 10−71 N, and setting Fge = GeMe2/r2 yields
- Ge = −6.68541 × 10−11 C·V·m/kg2
against the accepted 6.67259(85) × 10−11 m3/kg·s2 of the time — agreement to 0.19%. A note appended by Tesfatsion in June 2010 verifies that the units C·V·m/kg2 are indeed identical to m3/kg·s2.
Extension to bodies
To pass from two electrons to two arbitrary bodies, Spears introduces a second pure number A, the ratio of the body-to-body capacitance to the electron-to-electron capacitance at the same spacing: A = R1R2/Re2. He then asserts the proportionality C/Ce = R/Re = M/Me for every object, so that A = M1M2/Me2 and Fg = −6.68541 × 10−11 M1M2/r2. Newton's law is thus recovered in form as well as magnitude, and Spears emphasises that this was arrived at "without any reference to Newton's gravity force expression". The same relation applied to the proton gives Rp/Re = Mp/Me = P.
A variable G
Carrying the permittivities through the derivation gives Fg = [KQVA/2r] × ε122/ε1ε3, hence G = G0 ε122/ε02. Because dense matter is supposed to present an elevated effective permittivity to these minute fields, the measured G should depend on what the path between the test masses passes through — which Spears offers as the explanation for the spread among laboratory determinations, then ranging from Fitzgerald's 6.6656 × 10−11 to Michaelis's 6.7154 × 10−11. He points to the 1988 tower-gravity measurements of Eckhardt and colleagues, which found a slight extra fall-off of weight with height, as support.
The paper is unusually frank about its own history. Spears records that the "biggest obstacle" raised by readers of the 1991 book was "an apparent inability to convert from one system of units to another"; that a second book in 1993 attempted a different formulation requiring "an arbitrary selection of the effective radius of the electron"; that this was later judged "a terrible waste of three years"; and that the resolution, worked out in correspondence with the engineer Trevor Silvey, was the claim that K "is a pure number that stays the same in all systems of units for the physical system defined".
Assessment
The internal arithmetic is correct. Every number in the chain reproduces on recomputation: K = 4πε0Re2 = 8.8353 × 10−40, V1x = 7.8380 × 10−13 V, Fge = 5.5477 × 10−71 N and Ge = 6.6855 × 10−11. The whole construction collapses to a single closed form,
- Ge = e6 / [2(1 + Mp/Me)(4πε0)2 Me4 c4]
which evaluates with current CODATA constants to 6.68546 × 10−11. Spears is also right that the ratio he obtains is the right order: his force is 2.405 × 10−43 times the Coulomb force between two electrons, against the true gravitational ratio of 2.401 × 10−43.
But the agreement is an artefact of measuring length in metres. K is not a pure number. It is defined as (number of metres)/(number of darafs), and while the daraf count is a property of the capacitor and does not change with the length unit, the metre count does. Redo the identical calculation in centimetres and K becomes 8.8353 × 10−38, and Ge comes out 104 times its metre-based value — whereas converting a genuine G from m3/kg·s2 to cm3/kg·s2 requires a factor of 106. The result is wrong by a hundredfold as soon as the unit of length is changed. This is precisely the objection Spears records his readers making for twenty years, and the "resolution" he finally adopted — the assertion that K is invariant — is the one step in the paper that is simply false. Tesfatsion's appended note verifies that C·V·m/kg2 and m3/kg·s2 are the same units, which is true but answers a different question: the units of the answer are consistent, the numerical value is not.
Seen structurally, the derivation multiplies the real electrostatic force by an adjustable dimensionless factor of order 10−40 and identifies the product with gravity. The physical gloss is that the separation r = 1 m in F = QV/2r is replaced by r* = r/K ≈ 1.1 × 1039 m — some 1012 times the radius of the observable universe — described as "the length in metres of one daraf". (The paper's own bookkeeping here is inconsistent: it elsewhere states that "each daraf corresponds to 8.83538 × 10−40 meters", which is the reciprocal of the r* its force formula requires.) There is no independent argument that the daraf has a length, and the factor K does no work except to bring the number down to the size wanted.
The auxiliary assumptions conflict directly with measurement. Rp/Re = Mp/Me makes the proton's effective radius 1836 × 2.818 × 10−15 m ≈ 5.2 × 10−12 m. The measured proton charge radius, from both electron-proton scattering and the muonic-hydrogen Lamb shift, is 0.841 fm — six thousand times smaller than the electron's classical radius, not eighteen hundred times larger. Worse, effective radius proportional to mass makes a 1 kg mass 3.1 × 1015 m across and the Earth 1.9 × 1040 m across, while the capacitance formula C12 = 4πε12R1R2/r on which everything rests is stated in the paper itself to require "r12 much greater than the radii". The theory therefore violates its own validity condition by forty orders of magnitude for every macroscopic body it is applied to — which is every body anyone has ever weighed.
Two smaller internal problems. The energy stored in a capacitor is given correctly in §2 as Q2/2C, but the electron's rest energy is set equal to Qe2/Ce without the factor of two, a discrepancy the paper does not remark on. And "force is the energy divided by the distance" is not generally true — force is the derivative of energy with respect to distance — which for a 1/r capacitive energy happens to give the right magnitude but the wrong reasoning.
Finally, the accuracy claim has not aged well. In 1999 the spread among published G determinations was about 0.75%, and a theoretical value 0.19% high could reasonably be said to fall inside it. The CODATA value is now 6.67430(15) × 10−11, a relative uncertainty of 2.2 × 10−5; Spears's 6.68546 × 10−11 is 0.167% high, roughly 75 times that uncertainty, and is excluded. The particular outlier that made the 1990s spread look large — the Michaelis PTB value of 6.7154 × 10−11 — was subsequently traced to an instrumental effect and withdrawn. The Eckhardt tower-gravity anomaly of 1988 was likewise not confirmed; the excess gradient was resolved as inadequate modelling of local terrain and density rather than a new effect. And the central prediction that G varies with the permittivity of the intervening material is testable and fails: the same G that Cavendish-type balances measure through air and through their own apparatus also fits the Moon's orbit, lunar laser ranging and the planetary ephemerides, where the path is vacuum, and the geocentric gravitational parameter GM⊕ is known to about one part in 109 with no such discrepancy.
What remains attractive is the ambition and the honesty. Spears set out an explicit, fully numerical model, published the objections raised against it, abandoned a formulation he had spent three years on when it proved arbitrary, and named the exact difficulty — unit conversion — that turns out to be fatal.