On the Gravity Force

Scientific Paper
Title	On the Gravity Force
Read in full	Link to paper
Author(s)	Felix F Gorbatsevich
Keywords	gravity, force, Gravitational attraction, gravitational constant, gravitational field
Published	2011
No. of pages	12

Read the full paper here

Abstract

An action of a gradient medium on the body immersed into it is considered. Bodies of different size that are in a gradient medium are demonstrated to acquire the same acceleration. On the basis of the concept of the ether medium representing a regular spatial lattice consisting of particles equal in size but opposite in sign, the mechanism of gravitational attraction of physical bodies is considered. It is shown that the gradient of the gravitational field established by a physical body in the ether medium is similar to the action of the gradient medium on the immersed body. Creating the gradient of the ether elastic pressure by a physical body in the vicinity of another physical body that also creates the gradient of the ether elastic pressure in the vicinity of the first body results in a rise of an attractive force called gravitation. The closeness of the experimental gravitational constant and the value obtained from the theoretical analysis indicates that the approach we have developed is fruitful and adequate.

Overview

Felix Gorbatsevich, a geophysicist at Apatity on the Kola Peninsula, here applies the "non-empty ether" model set out in his earlier monographs to the problem of gravitation. The paper opens by cataloguing the profusion of existing gravitational theories — scalar, bimetric, quasi-linear, tensor, scalar-tensor, vector-tensor, non-metric — as evidence that "gravitation is the only fundamental interaction for which a noncontradictory theory has not been developed so far", and by noting that the gravitational constant stands alone among the fundamental constants in having no established link to any of the others. Supplying that link is the paper's declared goal.

The mechanism proposed is a buoyancy mechanism. The ether is taken to be a dense cubic lattice of equal-sized particles of alternating positive and negative charge, held rigidly together by their mutual electrical attraction. Matter is not immersed *in* this lattice in the ordinary sense: the strong fields near nuclei and electrons expel the ether entirely, so each elementary particle is a small void — the physical counterpart of the empty, thin-walled sphere used in the paper's opening thought experiment. Two such voids each disturb the lattice around the other, each finds itself in a pressure gradient established by its neighbour, and each is pushed toward the region of looser, lower-density ether. That mutual push is gravity. The scheme therefore belongs to the push-gravity tradition of Georges-Louis Le Sage and, as the paper points out, to a suggestion of Newton himself that the Archimedean principle might underlie gravitational attraction — but with an elastic charge lattice rather than a flux of corpuscles doing the pushing.

The argument

Buoyancy in a linear pressure gradient

The paper first works out, from scratch, the force on an empty thin-walled sphere of radius R in a medium of density δ whose pressure rises linearly with depth, P = nt. Resolving the surface force into components, the horizontal parts cancel by symmetry and the vertical parts do not, because points on the lower hemisphere lie deeper than their counterparts above. Integrating the vertical component over each hemisphere gives

F_l = (5/3)πqδR³ for the lower hemisphere and F_u = (1/3)πqδR³ for the upper, opposed to it

so that the net force is F = F_l − F_u = (4/3)πR³qδ, i.e. exactly F = −Vqδ with V the sphere's volume. The paper notes with satisfaction that this is Archimedes' principle recovered: "a body immersed in a gradient medium experiences the buoyant force equal to the volume of the displaced medium". It further observes that displacing the sphere a hundred radii deeper changes nothing, provided the medium is incompressible.

Why all bodies fall alike

From F = −Vqδ the paper takes the acceleration to be q = −F/Vδ. A second body of volume KV feels a force K times larger, so its acceleration is KVqδ/KVδ = q — unchanged. This yields what the paper italicises as its central conclusion: bodies of different volumes that are in the same gradient medium acquire the same acceleration.

The link to Galileo is then drawn. A lead pellet and a feather fall together in an evacuated tube; divide either body into pieces and the pieces fall together too; continue the division down to atoms and the result must still hold. Therefore, the paper argues, the gravitational field must act on *every* massive element of a body, not on its outer surface. Had it acted on the surface, a low-density body would be accelerated more strongly than a dense one of equal volume, and the observed correspondence between inertial and gravitational mass — confirmed by Eötvös and by Dicke, both cited — would fail. Only the ether volume expelled by the body's constituent particles matters; the body's external volume and bulk density are irrelevant.

Structure of the ether and the inverse square

The lattice picture (Fig. 2) is defended by appeal to electron–positron pair creation in vacuum under high-energy bombardment, taken as direct evidence that opposite charges are already present there. Near an elementary mass the lattice cannot keep its regular packing (Fig. 3): contacts between neighbouring opposite charges are broken, the structure is "loosened", and the loosening diminishes with distance.

The 1/R² falloff is argued by counting particles on concentric shells. If a circle of circumference L₁ = n₁d holds n₁ ether particles of diameter d, the next shell inward has radius R₁ − d and therefore holds n₁ − 2π particles, so a handful of particles per layer go uncompensated and a partial "vacuum of the ether medium" opens up. For the k-th layer the paper writes the looseness factor

Δ_k = (n₁ − 2kπ)/n₁ = 1 − 2kπ/n₁   (11)

and then asserts that the looseness falls off in proportion to the growth of the spherical surface area, so that the pressure on a test body rises as the square of the distance and its gradient falls as the inverse square.

From the ether density to the gravitational constant

The force on a single elementary particle expelling ether volume V_i is written F_i = τδV_i, with τ a proportionality factor absorbing the uncertainty in V_i and the unlike dimensionality of the ether density. That density is taken from the author's earlier work to be the magnetic constant itself,

δ = μ₀ = 1.25664×10⁻⁶ (m kg s⁻² A⁻²)   (13)

Since each of two masses sits in the gradient created by the other, the mutual force acquires two factors of τδ and one of 1/R²:

F_D = −τ²δ²V₁V₂/R²   (14)

Taking the expelled volumes as spheres, V = (4/3)πr³, gives

F_D = −2.771×10⁻¹¹ τ²r₁³r₂³/R² N   (15)

Set against Newton's law F_T = −GM₁M₂/R² with G = 6.6742×10⁻¹¹, the two coefficients are of the same order; the shortfall is 3.903×10⁻¹¹, and the numbers coincide if the free multiplier is

ψ = τ²r⁶ = 2.408   (19)

The paper offers three reasons why ψ should differ from unity: the ether density carries electromagnetic rather than mechanical dimensions; the lattice is already rarefied in the neighbourhood of an elementary mass; and r can only be an effective radius averaged over the whole ensemble of nuclei and electrons in a macroscopic body, which is "not a single volume, but a set of volumes". A concluding corollary is that since the ether transmits the gradient, gravitational influence propagates at the speed of electromagnetic oscillations in the ether — the speed of light.

Assessment

The paper's strongest section is its first. The hemispherical integration is done honestly and the numbers check: with the prefactor 2πqδR³, the lower hemisphere gives ∫sinα cosα dα + 2∫sin²α cosα dα = 1/2 + 2/3 = 5/6 and the upper 1/2 − 1/3 = 1/6, whose difference is 2/3, reproducing (4/3)πR³qδ exactly. The numerical chain at the end is also internally consistent: μ₀²[(4/3)π]² = 2.7707×10⁻¹¹, the quoted shortfall 6.6742 − 2.771 = 3.903 is right, and 6.6742/2.771 = 2.409 gives ψ. Whatever one thinks of the physics, the arithmetic was done and done correctly, which is not always the case in this literature. The underlying intuition — that an inverse-square attraction can be produced by shadowing or rarefaction in a pervasive medium — has a long and respectable history, and the paper is right that Newton entertained something like it.

The difficulties are structural. The "important conclusion" that all bodies acquire the same acceleration is obtained by dividing the buoyant force by the mass of the displaced medium, Vδ, rather than by the body's own inertial mass. Real buoyancy gives a = (ρ_med/ρ_body − 1)g, which manifestly does depend on the body's density — a cork and a stone do not rise and fall alike in water. The universality claimed in Eq. (10) therefore holds only if every body's inertia is exactly the mass of the ether it expels, which is not derived anywhere; it is the equivalence of inertial and gravitational mass assumed, not explained, in a paper that presents it as explained.

The inverse-square law is likewise asserted rather than derived. Equation (11) makes the looseness Δ_k linear in the layer index, hence linear in distance, whose gradient would be constant; the 1/R² is then obtained from a quite separate appeal to the growth of spherical surface area, with no demonstration that the two accounts agree. The shell-counting argument is also two-dimensional — circumferences, not spherical surfaces — and its conclusion that the ether grows denser with distance from a mass sits awkwardly beside the statement that the pressure on a test body "will increase proportionally to the squared distance", which read literally would make gravity stronger far away.

The numerical agreement that the conclusion rests on is the weakest link of all, for a reason the paper half-concedes. It admits that τ²r₁³r₂³ "should be given dimensionality m⁻⁴ kg⁻¹ s⁴ A⁴" for the result to come out in newtons — that is, the free factor is not a pure number at all but a dimensional fudge chosen to convert an electromagnetic quantity into a mechanical one. Worse, in the SI in force when the paper was written, μ₀ was defined as exactly 4π×10⁻⁷, so the coefficient 2.771×10⁻¹¹ is precisely (4π)⁴/9 × 10⁻¹⁴: a number manufactured out of the 1948 definition of the ampere and the choice of the metre and kilogram. Compute the same expression in Gaussian units, or after the 2019 SI redefinition, and the "closeness" to G evaporates. A coincidence that depends on a unit convention cannot bear the weight of the abstract's claim that the approach is thereby shown "fruitful and adequate". The point is sharpened by ψ itself: with r the effective radius of a nucleon, of order 10⁻¹⁵ m, r⁶ is of order 10⁻⁹⁰, so τ must be of order 10⁴⁵ — an unexplained number the paper never evaluates.

Finally, making the force proportional to expelled volume rather than to mass has a testable consequence the paper does not confront. Nuclear binding energy contributes about 0.8 per cent of the mass of iron but no additional nucleons, and electrons contribute volume without appreciable mass, so a volume-coupled gravity should show composition-dependent violations of universal free fall at roughly the percent level. Torsion-balance tests of exactly the kind the paper cites approvingly — Eötvös, and the modern Eöt-Wash measurements — bound such violations below one part in 10¹³. The paper invokes those experiments as support while proposing a coupling they exclude. Nothing is said either about how a rigid charge lattice that transmits transverse light waves avoids dragging the planets, the classical objection to every mechanical ether, nor about the perihelion and light-deflection tests that any replacement for general relativity must reproduce.

See also

• Felix F Gorbatsevich
• Aether
• Gravity
• Push Gravity
• Georges-Louis Le Sage
• Equivalence Principle
• Inertia
• Mass
• Vacuum
• Isaac Newton