Did Einstein Cheat? How Einstein Solved the Maxwell Analogy Problem
| Scientific Paper | |
|---|---|
| Title | Did Einstein Cheat? How Einstein Solved the Maxwell Analogy Problem |
| Read in full | Link to paper |
| Author(s) | Thierry De Mees |
| Keywords | gravity, gravity repulsion, relativity, gyrotation, Mercury perihelion, light bending, gravitomagnetism, Einstein, angular momentum |
| Published | 2010 |
| Journal | General Science Journal |
| No. of pages | 13 |
Read the full paper here
Abstract
Since one century, Gravitation has been in the spell of Einstein's Relativity Theory. Although during decades, dozens of scientists have provided evidences for the incorrectness of this theory. And often successfully, but without finding a sympathetic ear. Here we will discover what is wrong with the theory, and what brings a lot of scientists -in spite of that- to not dump it. We will not only discover that the Relativity Theory of Einstein is a tricked variant of the authentic Gravitation Theory, but we will also be able to form an idea about how and why Einstein did this. "Did Einstein Cheat?" is no attack on the person of Einstein, or on its working method. For that the reasons are too few. But it is a beautiful example, in these times, of a too long idolatry of a theory, just like it was the time before Galileo in astronomy and the time before Vesalius in medicine. Most remarkable is that the correct Gravitation Theory is an older theory than the Relativity Theory itself. In "Did Einstein Cheat?" both theories are examined and compared, put in their historical and scientific context, and applied on some essential physical phenomena: the progress of the perihelion of Mercury and the bending of the light close to the sun.
Overview
Written in December 2004 and updated in October 2010, this paper by the Belgian engineer Thierry De Mees carries the fuller subtitle "How Einstein solved the advance of Mercury's perihelion and the gyrotational bending of light." It is a comparative study of two rival accounts of gravitation: General Relativity, and the Maxwell Analogy — the proposal, made by Oliver Heaviside in 1893, that gravitation obeys equations formally identical to Maxwell's, with mass replacing charge and a second, magnetic-like field (which De Mees calls gyrotation) generated by moving mass. De Mees's central historical point is that the analogy is the older theory, and that it lost to relativity for a contingent reason: with the astronomical knowledge of 1900 it could account for only about one twelfth of Mercury's anomalous 43″ per century.
The paper's argument has three parts. First, drawing on Oleg D Jefimenko and on the self-taught engineer James A. Green, it argues that General Relativity is internally inconsistent and that its two classic solar-system successes were calibrations rather than predictions. Second, it supplies what Einstein's contemporaries could not: a source for the missing term in Mercury's precession, namely the Sun's ~235 km/s orbital motion through the Milky Way's gravitational field, which was unknown in 1915. Third, it recomputes the deflection of starlight past the Sun from the analogy, obtaining Einstein's doubled value plus two additional terms. The title question is left deliberately open — De Mees writes that "probably we should not judge Einstein too quickly" and that consciously cheating "is still another thing."
The argument
The Maxwell analogy for gravitation
The framework is set out as a Maxwell-form system in which charge is replaced by mass, the magnetic field by the gyrotation field Ω, and the constants by G−1 = 4πζ. The force law becomes F ⇐ m(g + v × Ω), with ∇·g ⇐ ρ/ζ, c2∇×Ω ⇐ j/ζ + ∂g/∂t, ∇·Ω = 0 and ∇×g ⇐ −∂Ω/∂t. De Mees deliberately writes ⇐ rather than = to insist that the right-hand side causes the left — a Jefimenko-derived stricture that only moving masses, never fields by themselves, induce these effects. Wave propagation at speed c follows from c2 = 1/(ζτ) with τ = 4πG/c2.
Two results are imported from Jefimenko. The first is that the analogy forms a genuinely coherent dynamics: energies, forces, linear and angular momenta are mutually derivable by pure mathematical manipulation in a way Newton's laws alone did not permit. The second concerns clocks. Jefimenko constructs charge-and-ring arrangements whose periods dilate as T = T0(1 − v2/c2)−1/2, but also others giving exponents of −5/4 and −3/4. De Mees draws the moral that "the clock type is determinative for its time delay" — if an atomic clock behaves relativistically, that is a fact about the structure of the atom, not a universal law of time.
Green's coefficient objection
The paper's sharpest technical claim comes from James A. Green. Starting from Einstein's field equations and truncating at second post-Newtonian order, Green recovers the Maxwell-form potential equations □2φ = ρ/ζ, □2A = τj, Ω = ∇×A, g = −∇φ − ∂A/∂t — but only if c2 is replaced at one step by 4(ζτ)−1 rather than (ζτ)−1. Carrying that factor of four through yields 4 div j = −∂ρ/∂t, in direct contradiction with the continuity equation. The same conclusion is reached by a second route, through the Lorentz gauge c2div A = −∂φ/∂t. De Mees's verdict is unqualified: "the General Relativity Theory is not consistent with itself", and the discrepancy is a factor of four, not a truncation error.
Mercury: the missing velocity
De Mees rewrites Einstein's precession formula δ = 24π2a2/[T2c2(1−e2)] using Kepler's third law to get δ = 6GM/[ac2(1−e2)], and for small eccentricity simply δ = 6v2/c2 where v is the orbital speed. He then asks what the analogy gives.
Here the paper makes its most characteristic move. Heaviside and Jefimenko, he argues, both erred in referring the induced field to the observer; what matters is the Local Absolute Velocity with respect to the "local stationary gravitation field", since "only gravitation fields can be regarded as locally immobile references." The Sun's 26-day spin is far too slow to matter. But the Sun orbits the galactic centre — De Mees computes ~240 km/s from the Maxwell analogy applied to the Milky Way (assuming a bulge of 10% of galactic mass and 10,000 light-years across), against a literature value of 220–250 km/s. Taking v1 = 235 km/s for the Sun and v2 = 47.9 km/s for Mercury gives v12 = 24v22. The gyrotational term in the force expansion then reads −Fα = GmM'v12cos2α/(2r2c2), which becomes 12GmMv22cos2α/(r2c2); averaging over the orbit yields 6GmMv22/(r2c2), that is δ = 6v22/c2 — "exactly the value which was obtained using the Relativity Theory."
To his credit De Mees immediately concedes the circularity: "Of course we have chosen v1 exactly equal to 235 km/s, in order to obtain the aimed result," adding that the true speed should probably be somewhat lower, the eccentricity restored, and planetary perturbations recomputed since they too exert gyrotational forces.
Light bending, and three terms instead of one
For light the Newtonian gravitational term is dropped, since the rest mass is zero; only the gyrotation of a mass flow at speed c is retained. Using Jefimenko's result for the gyrotation of a beam, with m = πρa2 per unit length, De Mees obtains Ω = −2Gm/(r2c) and hence a force per unit length FΩ = −2GmM/r2 — precisely double the Newtonian value, matching Einstein's 1.75″ Rz/r rather than his own 1911 value of 0.875″. Two further terms follow: one in v12cos2αcos2φ depending on the orientation of the light path relative to the galactic equator, and one in ω cos ϕ cos θ depending on solar latitude and the Sun's differential rotation. The last is signed: attractive on one limb and repulsive on the other, because of the Sun's spin direction. De Mees points to reported radio-wave measurements showing agreement near the solar poles and slight deviation toward the equator as the kind of latitude dependence relativity does not predict.
Why relativity won
The closing sections are historical and sociological. Einstein, De Mees argues, had three constraints — the Newtonian limit, light bending, Mercury — plus the need to accommodate Lorentz contraction after Michelson–Morley, and knew the analogy could not deliver Mercury with 1915's data. General Relativity's mathematical form "virtually deleted all tracks of the Maxwell Analogy", and its generality lets any mathematically valid solution count as a possible reality. He credits it with real achievements — the prediction of black holes and wormholes long before observation, a genuinely new cosmological picture — while noting that non-rotating black holes and wormholes remain unfound, and that rotating black holes, which are observed, required extending the theory. He also cites his own earlier work claiming that disc-galaxy rotation obeys Kepler's laws and that dark mass "is a myth".
Assessment
The paper's real strength is that it identifies precisely what the Maxwell analogy needed in order to compete and then supplies it. That the analogy failed on Mercury in 1900 for want of knowledge about the Galaxy is a legitimate and interesting historical observation, and looking for the missing term in the Sun's galactic motion is exactly the right instinct within the theory's own logic. The insistence on a "local stationary gravitation field" as the reference for velocity, rather than the observer, is a substantive correction to Heaviside and Jefimenko rather than a restatement, and it is what makes the calculation possible at all. Green's coefficient objection, if it survives scrutiny, is a serious technical charge rather than a rhetorical one — it is stated concretely, derived by two independent routes, and lands on a violation of mass continuity that anyone with the same tools can check. The light-bending section is genuinely predictive in a way the Mercury section is not: a solar-latitude-dependent deflection that changes sign between limbs is a distinguishing signature that General Relativity does not produce, and it is falsifiable.
The difficulties are correspondingly concentrated in the Mercury derivation, which is the paper's advertised centrepiece. De Mees's own admission that v1 = 235 km/s was "chosen exactly" to obtain the target result concedes that this is a fit, not a derivation — the very charge of calibration he levels at Einstein. Worse, it is a fit with a structural problem the paper does not confront: the anomalous precession of Mercury is not the only such measurement. Venus, Earth, Icarus and the binary pulsar PSR B1913+16 all show precessions matching the relativistic 6GM/ac2(1−e2) form, whose a-dependence follows automatically. A mechanism driven by the Sun's galactic velocity, which is the same for every planet, cannot reproduce that per-orbit scaling without further adjustment, and the paper tests only one planet. Similarly, the cos2α factor makes the effect depend on the orientation of Mercury's orbit relative to the galactic plane — a strong prediction that goes unexamined. The gyrotational light-bending calculation, meanwhile, treats a light ray as a mass flow with m per unit length while simultaneously setting the rest mass to zero, a step asserted rather than justified; the factor of two emerges from that choice, and no argument is offered for why the same substitution should not also be made in other contexts where it would give wrong answers. The Green objection deserves a caveat too: reading the post-Newtonian expansion as a claim about the numerical value of c in a wave equation conflates a gauge-and-units matter with a physical inconsistency, and the paper does not consider that possibility. Finally, the sociological explanation — relativity survived because "a complete army of scientists has been proliferated out of the Relativistic schools, almost such as new religions ever arose" — carries no argumentative weight and sits awkwardly beside the paper's own admission that the analogy could not, at the time, do the job.