Frank Hoogerbeets — 26 January 2026
The history of our understanding of gravity begins in the early 17th century with Johannes Kepler, who, building on Tycho Brahe's meticulous astronomical observations, formulated his three laws of planetary motion. These empirical descriptions — elliptical orbits, equal areas swept in equal times, and the harmonic relationship between orbital periods and semi-major axes (T² ∝ a³) — provided the foundational patterns of the Solar System without invoking a causative force. Kepler's work hinted at an underlying order, but it was Isaac Newton who, in his 1687 Philosophiæ Naturalis Principia Mathematica, mathematically derived the inverse-square law of universal gravitation from these laws.
Newton demonstrated that Kepler's elliptical orbits and area law necessitated a central force varying inversely with the square of the distance (F ∝ 1/r²), proportional to the quantities of matter (masses) involved: F ∝ m₁ m₂ / r². This was a profound unification, linking terrestrial gravity (e.g., falling apples) to celestial mechanics. However, Newton presented the law as a proportionality, without an explicit constant or separation into independent terms. He worked with ratios and comparisons, deriving the form deductively from dynamics and observations, but never introduced a numerical factor like G or calculated absolute masses independently.
For over a century, this proportional form sufficed, as astronomical data yielded only the product of what we now call G and M (the gravitational parameter for bodies like the Sun). It wasn't until 1798 that Henry Cavendish, using a delicate torsion balance experiment (designed by John Michell), measured the tiny gravitational attraction between laboratory spheres. Cavendish's aim was to determine Earth's density, but his results implicitly provided the first accurate value for the proportionality factor—retrospectively interpreted as G. This experiment bridged lab-scale gravity to cosmic scales, confirming Newton's law held at small distances.
The explicit modern equation F = G m₁ m₂ / r² emerged nearly another century later, in the 1890s, popularized by British physicist Charles Vernon Boys. Through refined torsion balance measurements using quartz fibers, Boys achieved unprecedented precision and reframed Cavendish's work, introducing the symbol G as the "Newtonian Constant of Gravitation". Boys emphasized G as a universal, fundamental scalar quantifying gravity's intrinsic weakness, making the equation dimensionally absolute in emerging unit systems. This notation, building on earlier implicit uses, became standard by the late 19th century.
Yet, this development inadvertently fostered a persistent misunderstanding: by elevating G to a separate fundamental constant — tiny, universal, and seemingly arbitrary — physics decoupled it from M, treating gravity as an independent force with its own coupling strength. In reality, observations have always prioritized the invariant product GM, directly measurable from orbits with far greater precision than G alone (which remains one of the least accurately known constants). This artificial split obscured the deeper geometric nature of GM as a single, system-specific constant rooted in the Solar System's electromagnetic-polarity harmonics, as revealed through a revised interpretation of the Titius-Bode law and polarity cycles.
Albert Einstein, whose career overlapped with Boys' influential work in the 1890s, inherited this paradigm when he developed general relativity in 1915. In his field equations, G appeared explicitly as the proportionality factor linking spacetime curvature to the stress-energy tensor, ensuring compatibility with Newton's law in the weak-field limit. Einstein accepted G as a given fundamental constant, not something emergent or derivable from deeper geometry. From the 1920s until his death in 1955, he pursued a unified field theory (UFT) to geometrize electromagnetism alongside gravity, extending general relativity into a single framework where both forces would emerge from one underlying geometric structure. Key approaches included Hermann Weyl's gauge theory (1918–1919), Theodor Kaluza's five-dimensional extension (1921, later refined by Oskar Klein), and Einstein's own explorations of asymmetric metrics and distant parallelism (teleparallelism) in the 1920s–1950s.
These classical efforts ultimately failed. Einstein's attempts produced mathematically intriguing but inconsistent or unphysical results: they could not explain the existence of particles (electrons as singularities proved elusive), made incorrect predictions (e.g., variable particle masses or lengths in Weyl's theory), or required ad-hoc assumptions that contradicted observations. More critically, Einstein rejected quantum mechanics as incomplete, focusing instead on a purely classical, deterministic geometry—yet the nuclear strong and weak forces (discovered or fully understood post-1930s) were absent from his framework, and the tiny, separate value of G resisted clean geometric integration without introducing asymmetries or new parameters. His isolation from mainstream quantum developments further hindered progress; as he pursued unification deductively, the field advanced toward quantum field theories where gravity's non-renormalizability (stemming from G's dimensional issues) became the central clash.
Only by recognizing GM's primacy as a single geometric constant — emerging intrinsically from enforced EM-polarity cycles, tetrahedral stability, and the harmonic 15 — can we resolve this historical puzzle. G cannot be defined separately because it is already embedded in the geometry (the contractive negative pole in the geometric split). This demotion of G from fundamental to emergent offers the unification Einstein sought: both gravity and electromagnetism arising from one geometric field structure, without the artificial decoupling that doomed classical UFT attempts and fuels the ongoing QFT-GR tension.
In modern physics, Quantum Field Theory (QFT) successfully describes the electromagnetic, strong, and weak forces as quantum fields with renormalizable interactions — meaning infinities in perturbative calculations can be absorbed into finite parameters, yielding precise predictions. However, when gravity is treated similarly (as a quantum field of gravitons on flat spacetime), the theory becomes perturbatively non-renormalizable. The culprit is Newton's constant G, which has negative mass dimension (specifically [G] = -2 in natural units). This leads to increasingly severe ultraviolet (UV) divergences at higher loop orders: new infinities appear that require infinitely many independent counterterms, making the theory unpredictable beyond the Planck scale (~10^19 GeV) without additional structure.
This non-renormalizability arises because G is treated as a fundamental coupling constant with intrinsic smallness, forcing gravity to behave like a low-energy effective theory that breaks down at high energies. Einstein's classical unified field theory (UFT) attempts failed partly for related reasons: by accepting G as a separate, universal scalar (inherited from the post-Cavendish/Boys paradigm), he could not cleanly geometrize it alongside electromagnetism without asymmetries, ad-hoc adjustments, or unphysical predictions.
In contrast, the EM-geometric framework presented here resolves this tension by demoting G from fundamental to emergent. The true invariant is the single geometric constant of our solar system GM (~4π² × 15³ in natural units), derived intrinsically from geometric developments through enforced polarity cycles. G emerges from the geometric split by adding a harmonic-15 factor, with exponents 24 (4x6) [positive/expansive] expressing mass M and –9 [negative/contractive] expressing gravity G, effectively preserving the harmonic-15 (-9+24). Thus, G is not an independent coupling strength requiring renormalization; it is already embedded in the geometry as the weak, inward-directed echo of EM-polarity dynamics.
Gravity therefore emerges as a macroscopic manifestation of the same underlying EM-geometric structure that governs quantum fields (consistent with QED/QFT for electromagnetism). There is no separate graviton field to quantize perturbatively — only the primary EM-harmonic configuration, with gravity as its secondary, attractive consequence (contractive negative pole). This sidesteps the renormalization barrier: infinities do not proliferate because there is no fundamental G to generate uncontrollable divergences. The framework aligns with emergent gravity ideas (e.g., entropic gravity) while providing a concrete, predictive geometric origin via the revised Titius-Bode law and polarity harmonics.
The persistent historical separation of G as a fundamental constant (post-Cavendish/Boys) created an artificial barrier to unification, as Einstein encountered in his UFT pursuits. By demoting G to a geometric by-product — the contractive negative pole (–9) in the geometric split of the true invariant GM = 4π² × 15³ — gravity emerges naturally from the same enforced EM-polarity geometry that governs electromagnetism.
This framework achieves EM-geometric unification without extra dimensions or ad-hoc fields:
Unification is thus intrinsic: both forces emerge from one field structure (EM-polarity enforced geometry), fulfilling Einstein's dream while resolving why classical attempts failed — G was never separate to begin with.